← Decimals convert small units to larger ones · Multiplicative Comparison and Unit Rate

Decimals convert small units to larger ones · 12 practice problems

5.MD.A.15.NBT.B.74.MD.A.2

Generated variants — 12

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 29.4 L

A car travels $52.5\ \text{km}$ in one hour. If the car uses $0.16\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $3$ hours and $30$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 52.5 km every hour and burns 0.16 L for each kilometre. It drives for 3 hours and 30 minutes. We need the petrol used.

Givens

Speed: 52.5 km per hour.
Fuel use: 0.16 L per km.
Driving time: 3 hours 30 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

30 minutes is 30 sixtieths of an hour, which comes out to a clean decimal.

30 \div 60 = 0.5,\quad 3 + 0.5 = 3.5\ \text{h}

The trip lasts 3.5 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

52.5 \times 3.5 = 183.75\ \text{km}

The car covers 183.75 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

183.75 \times 0.16 = 29.4\ \text{L}

It needs 29.4 L.

Answer: 29.4 L

4 · Reviewdoes it hold up?

Estimate: about 52 km/h for about 3.5 hours is roughly 184 km, and at 0.16 L/km that is near 29.4 L. The exact answer agrees.

Another way: Fuel per hour first: 52.5 x 0.16 = 8.4 L each hour, times 3.5 hours gives 29.4 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 3 h 30 min into 3.5 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 2 easy answer: 36.54 L

A car travels $58\ \text{km}$ in one hour. If the car uses $0.15\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $4$ hours and $12$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 58 km every hour and burns 0.15 L for each kilometre. It drives for 4 hours and 12 minutes. We need the petrol used.

Givens

Speed: 58 km per hour.
Fuel use: 0.15 L per km.
Driving time: 4 hours 12 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

12 minutes is 12 sixtieths of an hour, which comes out to a clean decimal.

12 \div 60 = 0.2,\quad 4 + 0.2 = 4.2\ \text{h}

The trip lasts 4.2 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

58 \times 4.2 = 243.6\ \text{km}

The car covers 243.6 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

243.6 \times 0.15 = 36.54\ \text{L}

It needs 36.54 L.

Answer: 36.54 L

4 · Reviewdoes it hold up?

Estimate: about 58 km/h for about 4.2 hours is roughly 244 km, and at 0.15 L/km that is near 36.5 L. The exact answer agrees.

Another way: Fuel per hour first: 58 x 0.15 = 8.7 L each hour, times 4.2 hours gives 36.54 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 4 h 12 min into 4.2 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 3 easy answer: 37.5765 L

A car travels $61.5\ \text{km}$ in one hour. If the car uses $0.13\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $4$ hours and $42$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 61.5 km every hour and burns 0.13 L for each kilometre. It drives for 4 hours and 42 minutes. We need the petrol used.

Givens

Speed: 61.5 km per hour.
Fuel use: 0.13 L per km.
Driving time: 4 hours 42 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

42 minutes is 42 sixtieths of an hour, which comes out to a clean decimal.

42 \div 60 = 0.7,\quad 4 + 0.7 = 4.7\ \text{h}

The trip lasts 4.7 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

61.5 \times 4.7 = 289.05\ \text{km}

The car covers 289.05 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

289.05 \times 0.13 = 37.5765\ \text{L}

It needs 37.5765 L.

Answer: 37.5765 L

4 · Reviewdoes it hold up?

Estimate: about 62 km/h for about 4.7 hours is roughly 289 km, and at 0.13 L/km that is near 37.6 L. The exact answer agrees.

Another way: Fuel per hour first: 61.5 x 0.13 = 7.995 L each hour, times 4.7 hours gives 37.5765 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 4 h 42 min into 4.7 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 4 easy answer: 24.96 L

A car travels $64\ \text{km}$ in one hour. If the car uses $0.12\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $3$ hours and $15$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 64 km every hour and burns 0.12 L for each kilometre. It drives for 3 hours and 15 minutes. We need the petrol used.

Givens

Speed: 64 km per hour.
Fuel use: 0.12 L per km.
Driving time: 3 hours 15 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

15 minutes is 15 sixtieths of an hour, which comes out to a clean decimal.

15 \div 60 = 0.25,\quad 3 + 0.25 = 3.25\ \text{h}

The trip lasts 3.25 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

64 \times 3.25 = 208\ \text{km}

The car covers 208 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

208 \times 0.12 = 24.96\ \text{L}

It needs 24.96 L.

Answer: 24.96 L

4 · Reviewdoes it hold up?

Estimate: about 64 km/h for about 3.2 hours is roughly 208 km, and at 0.12 L/km that is near 25.0 L. The exact answer agrees.

Another way: Fuel per hour first: 64 x 0.12 = 7.68 L each hour, times 3.25 hours gives 24.96 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 3 h 15 min into 3.25 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 5 medium answer: 22.218 L

A car travels $69\ \text{km}$ in one hour. If the car uses $0.14\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $2$ hours and $18$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 69 km every hour and burns 0.14 L for each kilometre. It drives for 2 hours and 18 minutes. We need the petrol used.

Givens

Speed: 69 km per hour.
Fuel use: 0.14 L per km.
Driving time: 2 hours 18 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

18 minutes is 18 sixtieths of an hour, which comes out to a clean decimal.

18 \div 60 = 0.3,\quad 2 + 0.3 = 2.3\ \text{h}

The trip lasts 2.3 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

69 \times 2.3 = 158.7\ \text{km}

The car covers 158.7 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

158.7 \times 0.14 = 22.218\ \text{L}

It needs 22.218 L.

Answer: 22.218 L

4 · Reviewdoes it hold up?

Estimate: about 69 km/h for about 2.3 hours is roughly 159 km, and at 0.14 L/km that is near 22.2 L. The exact answer agrees.

Another way: Fuel per hour first: 69 x 0.14 = 9.66 L each hour, times 2.3 hours gives 22.218 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 2 h 18 min into 2.3 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 6 medium answer: 9.72 L

A car travels $72\ \text{km}$ in one hour. If the car uses $0.09\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $1$ hours and $30$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 72 km every hour and burns 0.09 L for each kilometre. It drives for 1 hours and 30 minutes. We need the petrol used.

Givens

Speed: 72 km per hour.
Fuel use: 0.09 L per km.
Driving time: 1 hours 30 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

30 minutes is 30 sixtieths of an hour, which comes out to a clean decimal.

30 \div 60 = 0.5,\quad 1 + 0.5 = 1.5\ \text{h}

The trip lasts 1.5 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

72 \times 1.5 = 108\ \text{km}

The car covers 108 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

108 \times 0.09 = 9.72\ \text{L}

It needs 9.72 L.

Answer: 9.72 L

4 · Reviewdoes it hold up?

Estimate: about 72 km/h for about 1.5 hours is roughly 108 km, and at 0.09 L/km that is near 9.7 L. The exact answer agrees.

Another way: Fuel per hour first: 72 x 0.09 = 6.48 L each hour, times 1.5 hours gives 9.72 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 1 h 30 min into 1.5 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 7 medium answer: 14.4375 L

A car travels $75\ \text{km}$ in one hour. If the car uses $0.11\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $1$ hours and $45$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 75 km every hour and burns 0.11 L for each kilometre. It drives for 1 hours and 45 minutes. We need the petrol used.

Givens

Speed: 75 km per hour.
Fuel use: 0.11 L per km.
Driving time: 1 hours 45 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

45 minutes is 45 sixtieths of an hour, which comes out to a clean decimal.

45 \div 60 = 0.75,\quad 1 + 0.75 = 1.75\ \text{h}

The trip lasts 1.75 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

75 \times 1.75 = 131.25\ \text{km}

The car covers 131.25 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

131.25 \times 0.11 = 14.4375\ \text{L}

It needs 14.4375 L.

Answer: 14.4375 L

4 · Reviewdoes it hold up?

Estimate: about 75 km/h for about 1.8 hours is roughly 131 km, and at 0.11 L/km that is near 14.4 L. The exact answer agrees.

Another way: Fuel per hour first: 75 x 0.11 = 8.25 L each hour, times 1.75 hours gives 14.4375 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 1 h 45 min into 1.75 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 8 medium answer: 21.84 L

A car travels $78\ \text{km}$ in one hour. If the car uses $0.1\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $2$ hours and $48$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 78 km every hour and burns 0.1 L for each kilometre. It drives for 2 hours and 48 minutes. We need the petrol used.

Givens

Speed: 78 km per hour.
Fuel use: 0.1 L per km.
Driving time: 2 hours 48 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

48 minutes is 48 sixtieths of an hour, which comes out to a clean decimal.

48 \div 60 = 0.8,\quad 2 + 0.8 = 2.8\ \text{h}

The trip lasts 2.8 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

78 \times 2.8 = 218.4\ \text{km}

The car covers 218.4 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

218.4 \times 0.1 = 21.84\ \text{L}

It needs 21.84 L.

Answer: 21.84 L

4 · Reviewdoes it hold up?

Estimate: about 78 km/h for about 2.8 hours is roughly 218 km, and at 0.1 L/km that is near 21.8 L. The exact answer agrees.

Another way: Fuel per hour first: 78 x 0.1 = 7.8 L each hour, times 2.8 hours gives 21.84 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 2 h 48 min into 2.8 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 9 hard answer: 16.032 L

A car travels $83.5\ \text{km}$ in one hour. If the car uses $0.08\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $2$ hours and $24$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 83.5 km every hour and burns 0.08 L for each kilometre. It drives for 2 hours and 24 minutes. We need the petrol used.

Givens

Speed: 83.5 km per hour.
Fuel use: 0.08 L per km.
Driving time: 2 hours 24 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

24 minutes is 24 sixtieths of an hour, which comes out to a clean decimal.

24 \div 60 = 0.4,\quad 2 + 0.4 = 2.4\ \text{h}

The trip lasts 2.4 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

83.5 \times 2.4 = 200.4\ \text{km}

The car covers 200.4 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

200.4 \times 0.08 = 16.032\ \text{L}

It needs 16.032 L.

Answer: 16.032 L

4 · Reviewdoes it hold up?

Estimate: about 84 km/h for about 2.4 hours is roughly 200 km, and at 0.08 L/km that is near 16.0 L. The exact answer agrees.

Another way: Fuel per hour first: 83.5 x 0.08 = 6.68 L each hour, times 2.4 hours gives 16.032 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 2 h 24 min into 2.4 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 10 hard answer: 18.662 L

A car travels $86\ \text{km}$ in one hour. If the car uses $0.07\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $3$ hours and $6$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 86 km every hour and burns 0.07 L for each kilometre. It drives for 3 hours and 6 minutes. We need the petrol used.

Givens

Speed: 86 km per hour.
Fuel use: 0.07 L per km.
Driving time: 3 hours 6 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

6 minutes is 6 sixtieths of an hour, which comes out to a clean decimal.

6 \div 60 = 0.1,\quad 3 + 0.1 = 3.1\ \text{h}

The trip lasts 3.1 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

86 \times 3.1 = 266.6\ \text{km}

The car covers 266.6 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

266.6 \times 0.07 = 18.662\ \text{L}

It needs 18.662 L.

Answer: 18.662 L

4 · Reviewdoes it hold up?

Estimate: about 86 km/h for about 3.1 hours is roughly 267 km, and at 0.07 L/km that is near 18.7 L. The exact answer agrees.

Another way: Fuel per hour first: 86 x 0.07 = 6.02 L each hour, times 3.1 hours gives 18.662 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 3 h 6 min into 3.1 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 11 hard answer: 14.118 L

A car travels $90.5\ \text{km}$ in one hour. If the car uses $0.06\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $2$ hours and $36$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 90.5 km every hour and burns 0.06 L for each kilometre. It drives for 2 hours and 36 minutes. We need the petrol used.

Givens

Speed: 90.5 km per hour.
Fuel use: 0.06 L per km.
Driving time: 2 hours 36 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

36 minutes is 36 sixtieths of an hour, which comes out to a clean decimal.

36 \div 60 = 0.6,\quad 2 + 0.6 = 2.6\ \text{h}

The trip lasts 2.6 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

90.5 \times 2.6 = 235.3\ \text{km}

The car covers 235.3 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

235.3 \times 0.06 = 14.118\ \text{L}

It needs 14.118 L.

Answer: 14.118 L

4 · Reviewdoes it hold up?

Estimate: about 90 km/h for about 2.6 hours is roughly 235 km, and at 0.06 L/km that is near 14.1 L. The exact answer agrees.

Another way: Fuel per hour first: 90.5 x 0.06 = 5.43 L each hour, times 2.6 hours gives 14.118 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 2 h 36 min into 2.6 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.

Variant 12 hard answer: 8.93 L

A car travels $94\ \text{km}$ in one hour. If the car uses $0.05\ \text{L}$ of gasoline to travel $1\ \text{km}$ , how many liters of gasoline does it need to travel for $1$ hours and $54$ minutes at the same speed?

Show solution

1 · Understandwhat's really being asked

A car goes 94 km every hour and burns 0.05 L for each kilometre. It drives for 1 hours and 54 minutes. We need the petrol used.

Givens

Speed: 94 km per hour.
Fuel use: 0.05 L per km.
Driving time: 1 hours 54 minutes.

Unknowns

The litres of gasoline needed.

Constraints

Both rates are per hour and per kilometre, so the time must be in hours before either is used.

2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Convert the time to hours, use the speed to get kilometres, then use the fuel rate to turn kilometres into litres. Each step trades one unit for the next.

3 · Execute3 carry out the plan

1Write the time as hours in decimal form

#8 Analyze the Units 5.MD.A.1

54 minutes is 54 sixtieths of an hour, which comes out to a clean decimal.

54 \div 60 = 0.9,\quad 1 + 0.9 = 1.9\ \text{h}

The trip lasts 1.9 hours.

2Find the distance traveled

#7 Identify Subproblems 5.NBT.B.7

Kilometres per hour times hours leaves kilometres.

94 \times 1.9 = 178.6\ \text{km}

The car covers 178.6 km.

3Find the gasoline needed

#7 Identify Subproblems 5.NBT.B.7

Litres per kilometre times kilometres leaves litres.

178.6 \times 0.05 = 8.93\ \text{L}

It needs 8.93 L.

Answer: 8.93 L

4 · Reviewdoes it hold up?

Estimate: about 94 km/h for about 1.9 hours is roughly 179 km, and at 0.05 L/km that is near 8.9 L. The exact answer agrees.

Another way: Fuel per hour first: 94 x 0.05 = 4.7 L each hour, times 1.9 hours gives 8.93 L -- the same, with the multiplications reordered.

Standardsmin grade 5

5.MD.A.1 Convert among different-sized standard measurement units within a given system — Turning 1 h 54 min into 1.9 hours.
5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Multiplying the decimals for distance and then for fuel.
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Carrying distance, time and volume through one word problem.

💡Takeaway. A rate names the unit its partner must be in. Convert the minutes to hours first and each multiplication just swaps one unit for the next.