← Minutes are sixtieths of an hour, and a quotient that never ends is rounded · Multiplicative Comparison and Unit Rate

Minutes are sixtieths of an hour, and a quotient that never ends is rounded · 12 practice problems

6.NS.B.36.RP.A.26.RP.A.3

Generated variants — 12

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

Variant 1 easy answer: 37 km

A car travels 85 km85\ \text{km} in 22 hours 1818 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 85 km in 2 hours 18 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 85 km.
  • The time is 2 hours 18 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
18 minutes is 18 sixtieths of an hour.
18÷60=0.3,2 h 18 min=2.3 h18 \div 60 = 0.3,\quad 2\ \text{h}\ 18\ \text{min} = 2.3\ \text{h}
2.3 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
85÷2.3=36.9565…85 \div 2.3 = 36.9565\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
36.9565…→3736.9565\ldots \rightarrow 37
About 37 km an hour.
Answer: 37 km
4 · Reviewdoes it hold up?

Checking the size: 37 km an hour over 2.3 hours is about 85.1 km, which is the 85 km given, give or take the rounding.

Another way: Working in minutes first -- 85 km in 138 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 2 easy answer: 66.7 km

A car travels 100 km100\ \text{km} in 11 hour 3030 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 100 km in 1 hour 30 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 100 km.
  • The time is 1 hour 30 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
30 minutes is 30 sixtieths of an hour.
30÷60=0.5,1 h 30 min=1.5 h30 \div 60 = 0.5,\quad 1\ \text{h}\ 30\ \text{min} = 1.5\ \text{h}
1.5 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
100÷1.5=66.6667…100 \div 1.5 = 66.6667\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
66.6667…→66.766.6667\ldots \rightarrow 66.7
About 66.7 km an hour.
Answer: 66.7 km
4 · Reviewdoes it hold up?

Checking the size: 66.7 km an hour over 1.5 hours is about 100.0 km, which is the 100 km given, give or take the rounding.

Another way: Working in minutes first -- 100 km in 90 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 3 easy answer: 58.3 km

A car travels 105 km105\ \text{km} in 11 hour 4848 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 105 km in 1 hour 48 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 105 km.
  • The time is 1 hour 48 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
48 minutes is 48 sixtieths of an hour.
48÷60=0.8,1 h 48 min=1.8 h48 \div 60 = 0.8,\quad 1\ \text{h}\ 48\ \text{min} = 1.8\ \text{h}
1.8 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
105÷1.8=58.3333…105 \div 1.8 = 58.3333\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
58.3333…→58.358.3333\ldots \rightarrow 58.3
About 58.3 km an hour.
Answer: 58.3 km
4 · Reviewdoes it hold up?

Checking the size: 58.3 km an hour over 1.8 hours is about 104.9 km, which is the 105 km given, give or take the rounding.

Another way: Working in minutes first -- 105 km in 108 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 4 easy answer: 37.9 km

A car travels 125 km125\ \text{km} in 33 hours 1818 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 125 km in 3 hours 18 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 125 km.
  • The time is 3 hours 18 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
18 minutes is 18 sixtieths of an hour.
18÷60=0.3,3 h 18 min=3.3 h18 \div 60 = 0.3,\quad 3\ \text{h}\ 18\ \text{min} = 3.3\ \text{h}
3.3 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
125÷3.3=37.8788…125 \div 3.3 = 37.8788\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
37.8788…→37.937.8788\ldots \rightarrow 37.9
About 37.9 km an hour.
Answer: 37.9 km
4 · Reviewdoes it hold up?

Checking the size: 37.9 km an hour over 3.3 hours is about 125.1 km, which is the 125 km given, give or take the rounding.

Another way: Working in minutes first -- 125 km in 198 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 5 medium answer: 40.8 km

A car travels 155 km155\ \text{km} in 33 hours 4848 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 155 km in 3 hours 48 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 155 km.
  • The time is 3 hours 48 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
48 minutes is 48 sixtieths of an hour.
48÷60=0.8,3 h 48 min=3.8 h48 \div 60 = 0.8,\quad 3\ \text{h}\ 48\ \text{min} = 3.8\ \text{h}
3.8 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
155÷3.8=40.7895…155 \div 3.8 = 40.7895\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
40.7895…→40.840.7895\ldots \rightarrow 40.8
About 40.8 km an hour.
Answer: 40.8 km
4 · Reviewdoes it hold up?

Checking the size: 40.8 km an hour over 3.8 hours is about 155.0 km, which is the 155 km given, give or take the rounding.

Another way: Working in minutes first -- 155 km in 228 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 6 medium answer: 88.9 km

A car travels 160 km160\ \text{km} in 11 hour 4848 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 160 km in 1 hour 48 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 160 km.
  • The time is 1 hour 48 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
48 minutes is 48 sixtieths of an hour.
48÷60=0.8,1 h 48 min=1.8 h48 \div 60 = 0.8,\quad 1\ \text{h}\ 48\ \text{min} = 1.8\ \text{h}
1.8 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
160÷1.8=88.8889…160 \div 1.8 = 88.8889\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
88.8889…→88.988.8889\ldots \rightarrow 88.9
About 88.9 km an hour.
Answer: 88.9 km
4 · Reviewdoes it hold up?

Checking the size: 88.9 km an hour over 1.8 hours is about 160.0 km, which is the 160 km given, give or take the rounding.

Another way: Working in minutes first -- 160 km in 108 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 7 medium answer: 91.7 km

A car travels 220 km220\ \text{km} in 22 hours 2424 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 220 km in 2 hours 24 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 220 km.
  • The time is 2 hours 24 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
24 minutes is 24 sixtieths of an hour.
24÷60=0.4,2 h 24 min=2.4 h24 \div 60 = 0.4,\quad 2\ \text{h}\ 24\ \text{min} = 2.4\ \text{h}
2.4 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
220÷2.4=91.6667…220 \div 2.4 = 91.6667\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
91.6667…→91.791.6667\ldots \rightarrow 91.7
About 91.7 km an hour.
Answer: 91.7 km
4 · Reviewdoes it hold up?

Checking the size: 91.7 km an hour over 2.4 hours is about 220.1 km, which is the 220 km given, give or take the rounding.

Another way: Working in minutes first -- 220 km in 144 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 8 medium answer: 58.5 km

A car travels 240 km240\ \text{km} in 44 hours 66 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 240 km in 4 hours 6 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 240 km.
  • The time is 4 hours 6 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
6 minutes is 6 sixtieths of an hour.
6÷60=0.1,4 h 6 min=4.1 h6 \div 60 = 0.1,\quad 4\ \text{h}\ 6\ \text{min} = 4.1\ \text{h}
4.1 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
240÷4.1=58.5366…240 \div 4.1 = 58.5366\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
58.5366…→58.558.5366\ldots \rightarrow 58.5
About 58.5 km an hour.
Answer: 58.5 km
4 · Reviewdoes it hold up?

Checking the size: 58.5 km an hour over 4.1 hours is about 239.8 km, which is the 240 km given, give or take the rounding.

Another way: Working in minutes first -- 240 km in 246 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 9 hard answer: 123.9 km

A car travels 285 km285\ \text{km} in 22 hours 1818 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 285 km in 2 hours 18 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 285 km.
  • The time is 2 hours 18 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
18 minutes is 18 sixtieths of an hour.
18÷60=0.3,2 h 18 min=2.3 h18 \div 60 = 0.3,\quad 2\ \text{h}\ 18\ \text{min} = 2.3\ \text{h}
2.3 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
285÷2.3=123.9130…285 \div 2.3 = 123.9130\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
123.9130…→123.9123.9130\ldots \rightarrow 123.9
About 123.9 km an hour.
Answer: 123.9 km
4 · Reviewdoes it hold up?

Checking the size: 123.9 km an hour over 2.3 hours is about 285.0 km, which is the 285 km given, give or take the rounding.

Another way: Working in minutes first -- 285 km in 138 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 10 hard answer: 112.1 km

A car travels 325 km325\ \text{km} in 22 hours 5454 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 325 km in 2 hours 54 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 325 km.
  • The time is 2 hours 54 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
54 minutes is 54 sixtieths of an hour.
54÷60=0.9,2 h 54 min=2.9 h54 \div 60 = 0.9,\quad 2\ \text{h}\ 54\ \text{min} = 2.9\ \text{h}
2.9 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
325÷2.9=112.0690…325 \div 2.9 = 112.0690\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
112.0690…→112.1112.0690\ldots \rightarrow 112.1
About 112.1 km an hour.
Answer: 112.1 km
4 · Reviewdoes it hold up?

Checking the size: 112.1 km an hour over 2.9 hours is about 325.1 km, which is the 325 km given, give or take the rounding.

Another way: Working in minutes first -- 325 km in 174 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 11 hard answer: 79.6 km

A car travels 390 km390\ \text{km} in 44 hours 5454 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 390 km in 4 hours 54 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 390 km.
  • The time is 4 hours 54 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
54 minutes is 54 sixtieths of an hour.
54÷60=0.9,4 h 54 min=4.9 h54 \div 60 = 0.9,\quad 4\ \text{h}\ 54\ \text{min} = 4.9\ \text{h}
4.9 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
390÷4.9=79.5918…390 \div 4.9 = 79.5918\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
79.5918…→79.679.5918\ldots \rightarrow 79.6
About 79.6 km an hour.
Answer: 79.6 km
4 · Reviewdoes it hold up?

Checking the size: 79.6 km an hour over 4.9 hours is about 390.0 km, which is the 390 km given, give or take the rounding.

Another way: Working in minutes first -- 390 km in 294 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.
Variant 12 hard answer: 105.1 km

A car travels 410 km410\ \text{km} in 33 hours 5454 minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Show solution
1 · Understandwhat's really being asked

A car covers 410 km in 3 hours 54 minutes at a steady speed. We want its kilometres per hour, to one decimal place.

Givens
  • The distance is 410 km.
  • The time is 3 hours 54 minutes.
  • The speed is steady.
Unknowns
  • The distance covered in one hour.
Constraints
  • The answer is wanted to one decimal place.
2 · Planchoose the strategy

#8 Analyze the Units · also uses: #7 Identify Subproblems#11 Work Backwards

The time cannot be divided by as it stands. Turn the minutes into a decimal fraction of an hour -- sixtieths, not hundredths -- and then divide, rounding at the end because the quotient does not stop.

3 · Execute3 carry out the plan

1Turn the minutes into part of an hour

#8 Analyze the Units 6.RP.A.3
54 minutes is 54 sixtieths of an hour.
54÷60=0.9,3 h 54 min=3.9 h54 \div 60 = 0.9,\quad 3\ \text{h}\ 54\ \text{min} = 3.9\ \text{h}
3.9 hours, in one number.

2Divide the distance by the time

#7 Identify Subproblems 6.RP.A.2
That is what kilometres per hour means.
410÷3.9=105.1282…410 \div 3.9 = 105.1282\ldots
The digits do not stop.

3Round to one decimal place

#11 Work Backwards 6.NS.B.3
The second decimal place decides it.
105.1282…→105.1105.1282\ldots \rightarrow 105.1
About 105.1 km an hour.
Answer: 105.1 km
4 · Reviewdoes it hold up?

Checking the size: 105.1 km an hour over 3.9 hours is about 409.9 km, which is the 410 km given, give or take the rounding.

Another way: Working in minutes first -- 410 km in 234 minutes -- and multiplying by 60 gives the same rate, with the fraction moved to a different step.

Standardsmin grade 6
  • 6.NS.B.3 Fluently add, subtract, multiply, divide multi-digit decimals — Dividing decimals and rounding the result.
  • 6.RP.A.2 Understand unit rate a/b associated with a ratio — Reading the answer as kilometres per one hour.
  • 6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting minutes into a decimal part of an hour.
💡Takeaway. Minutes are sixtieths, not hundredths. And when a division does not stop, rounding is part of the answer.