Practice · How many times the unit quantity · Sensim Math

Variant 1 easy

An airplane travels $470\ \text{km}$ in one hour. If it flies at the same speed for $4$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 470 km every hour at a steady speed. Find how far it travels in 4 hours and 30 minutes.

Givens

The airplane travels 470 km in one hour
The speed stays the same
The flying time is 4 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 4 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 4 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 4 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 470 km, so 4 hours add 470 x 4 = 1880 km.

470 \times 4 = 1880 \text{ km}

4 equal hours is just multiplying the one-hour distance by 4.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 470 km, which is 470 / 2 = 235 km.

470 \div 2 = 235 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 4-hour part plus the half-hour part: 1880 + 235 = 2115 km.

1880 + 235 = 2115 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 2115 km

4 · Reviewdoes it hold up?

In 4 and a half hours the distance should be a bit more than 4 x 470 = 1880 and less than 5 x 470 = 2350. The answer 2115 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 4 h 30 min is 9 half-hours, and each half-hour covers 235 km, so 235 x 9 = 2115 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 470 x 4 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 4 full hours plus a half hour of the same speed!

Variant 2 easy

An airplane travels $548\ \text{km}$ in one hour. If it flies at the same speed for $5$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 548 km every hour at a steady speed. Find how far it travels in 5 hours and 30 minutes.

Givens

The airplane travels 548 km in one hour
The speed stays the same
The flying time is 5 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 5 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 5 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 5 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 548 km, so 5 hours add 548 x 5 = 2740 km.

548 \times 5 = 2740 \text{ km}

5 equal hours is just multiplying the one-hour distance by 5.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 548 km, which is 548 / 2 = 274 km.

548 \div 2 = 274 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 5-hour part plus the half-hour part: 2740 + 274 = 3014 km.

2740 + 274 = 3014 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 3014 km

4 · Reviewdoes it hold up?

In 5 and a half hours the distance should be a bit more than 5 x 548 = 2740 and less than 6 x 548 = 3288. The answer 3014 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 5 h 30 min is 11 half-hours, and each half-hour covers 274 km, so 274 x 11 = 3014 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 548 x 5 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 5 full hours plus a half hour of the same speed!

Variant 3 easy

An airplane travels $594\ \text{km}$ in one hour. If it flies at the same speed for $5$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 594 km every hour at a steady speed. Find how far it travels in 5 hours and 30 minutes.

Givens

The airplane travels 594 km in one hour
The speed stays the same
The flying time is 5 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 5 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 5 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 5 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 594 km, so 5 hours add 594 x 5 = 2970 km.

594 \times 5 = 2970 \text{ km}

5 equal hours is just multiplying the one-hour distance by 5.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 594 km, which is 594 / 2 = 297 km.

594 \div 2 = 297 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 5-hour part plus the half-hour part: 2970 + 297 = 3267 km.

2970 + 297 = 3267 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 3267 km

4 · Reviewdoes it hold up?

In 5 and a half hours the distance should be a bit more than 5 x 594 = 2970 and less than 6 x 594 = 3564. The answer 3267 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 5 h 30 min is 11 half-hours, and each half-hour covers 297 km, so 297 x 11 = 3267 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 594 x 5 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 5 full hours plus a half hour of the same speed!

Variant 4 medium

An airplane travels $652\ \text{km}$ in one hour. If it flies at the same speed for $7$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 652 km every hour at a steady speed. Find how far it travels in 7 hours and 30 minutes.

Givens

The airplane travels 652 km in one hour
The speed stays the same
The flying time is 7 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 7 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 7 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 7 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 652 km, so 7 hours add 652 x 7 = 4564 km.

652 \times 7 = 4564 \text{ km}

7 equal hours is just multiplying the one-hour distance by 7.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 652 km, which is 652 / 2 = 326 km.

652 \div 2 = 326 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 7-hour part plus the half-hour part: 4564 + 326 = 4890 km.

4564 + 326 = 4890 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 4890 km

4 · Reviewdoes it hold up?

In 7 and a half hours the distance should be a bit more than 7 x 652 = 4564 and less than 8 x 652 = 5216. The answer 4890 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 7 h 30 min is 15 half-hours, and each half-hour covers 326 km, so 326 x 15 = 4890 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 652 x 7 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 7 full hours plus a half hour of the same speed!

Variant 5 medium

An airplane travels $684\ \text{km}$ in one hour. If it flies at the same speed for $6$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 684 km every hour at a steady speed. Find how far it travels in 6 hours and 30 minutes.

Givens

The airplane travels 684 km in one hour
The speed stays the same
The flying time is 6 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 6 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 6 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 6 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 684 km, so 6 hours add 684 x 6 = 4104 km.

684 \times 6 = 4104 \text{ km}

6 equal hours is just multiplying the one-hour distance by 6.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 684 km, which is 684 / 2 = 342 km.

684 \div 2 = 342 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 6-hour part plus the half-hour part: 4104 + 342 = 4446 km.

4104 + 342 = 4446 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 4446 km

4 · Reviewdoes it hold up?

In 6 and a half hours the distance should be a bit more than 6 x 684 = 4104 and less than 7 x 684 = 4788. The answer 4446 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 6 h 30 min is 13 half-hours, and each half-hour covers 342 km, so 342 x 13 = 4446 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 684 x 6 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 6 full hours plus a half hour of the same speed!

Variant 6 medium

An airplane travels $732\ \text{km}$ in one hour. If it flies at the same speed for $3$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 732 km every hour at a steady speed. Find how far it travels in 3 hours and 30 minutes.

Givens

The airplane travels 732 km in one hour
The speed stays the same
The flying time is 3 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 3 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 3 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 3 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 732 km, so 3 hours add 732 x 3 = 2196 km.

732 \times 3 = 2196 \text{ km}

3 equal hours is just multiplying the one-hour distance by 3.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 732 km, which is 732 / 2 = 366 km.

732 \div 2 = 366 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 3-hour part plus the half-hour part: 2196 + 366 = 2562 km.

2196 + 366 = 2562 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 2562 km

4 · Reviewdoes it hold up?

In 3 and a half hours the distance should be a bit more than 3 x 732 = 2196 and less than 4 x 732 = 2928. The answer 2562 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 3 h 30 min is 7 half-hours, and each half-hour covers 366 km, so 366 x 7 = 2562 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 732 x 3 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 3 full hours plus a half hour of the same speed!

Variant 7 medium

An airplane travels $786\ \text{km}$ in one hour. If it flies at the same speed for $4$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 786 km every hour at a steady speed. Find how far it travels in 4 hours and 30 minutes.

Givens

The airplane travels 786 km in one hour
The speed stays the same
The flying time is 4 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 4 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 4 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 4 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 786 km, so 4 hours add 786 x 4 = 3144 km.

786 \times 4 = 3144 \text{ km}

4 equal hours is just multiplying the one-hour distance by 4.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 786 km, which is 786 / 2 = 393 km.

786 \div 2 = 393 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 4-hour part plus the half-hour part: 3144 + 393 = 3537 km.

3144 + 393 = 3537 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 3537 km

4 · Reviewdoes it hold up?

In 4 and a half hours the distance should be a bit more than 4 x 786 = 3144 and less than 5 x 786 = 3930. The answer 3537 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 4 h 30 min is 9 half-hours, and each half-hour covers 393 km, so 393 x 9 = 3537 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 786 x 4 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 4 full hours plus a half hour of the same speed!

Variant 8 hard

An airplane travels $838\ \text{km}$ in one hour. If it flies at the same speed for $3$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 838 km every hour at a steady speed. Find how far it travels in 3 hours and 30 minutes.

Givens

The airplane travels 838 km in one hour
The speed stays the same
The flying time is 3 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 3 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 3 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 3 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 838 km, so 3 hours add 838 x 3 = 2514 km.

838 \times 3 = 2514 \text{ km}

3 equal hours is just multiplying the one-hour distance by 3.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 838 km, which is 838 / 2 = 419 km.

838 \div 2 = 419 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 3-hour part plus the half-hour part: 2514 + 419 = 2933 km.

2514 + 419 = 2933 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 2933 km

4 · Reviewdoes it hold up?

In 3 and a half hours the distance should be a bit more than 3 x 838 = 2514 and less than 4 x 838 = 3352. The answer 2933 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 3 h 30 min is 7 half-hours, and each half-hour covers 419 km, so 419 x 7 = 2933 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 838 x 3 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 3 full hours plus a half hour of the same speed!

Variant 9 hard

An airplane travels $864\ \text{km}$ in one hour. If it flies at the same speed for $4$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 864 km every hour at a steady speed. Find how far it travels in 4 hours and 30 minutes.

Givens

The airplane travels 864 km in one hour
The speed stays the same
The flying time is 4 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 4 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 4 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 4 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 864 km, so 4 hours add 864 x 4 = 3456 km.

864 \times 4 = 3456 \text{ km}

4 equal hours is just multiplying the one-hour distance by 4.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 864 km, which is 864 / 2 = 432 km.

864 \div 2 = 432 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 4-hour part plus the half-hour part: 3456 + 432 = 3888 km.

3456 + 432 = 3888 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 3888 km

4 · Reviewdoes it hold up?

In 4 and a half hours the distance should be a bit more than 4 x 864 = 3456 and less than 5 x 864 = 4320. The answer 3888 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 4 h 30 min is 9 half-hours, and each half-hour covers 432 km, so 432 x 9 = 3888 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 864 x 4 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 4 full hours plus a half hour of the same speed!

Variant 10 hard

An airplane travels $916\ \text{km}$ in one hour. If it flies at the same speed for $2$ hours and $30$ minutes, find how many $\text{km}$ it can travel.

Your answer

Show solution

1 · Understandwhat's really being asked

An airplane flies 916 km every hour at a steady speed. Find how far it travels in 2 hours and 30 minutes.

Givens

The airplane travels 916 km in one hour
The speed stays the same
The flying time is 2 hours and 30 minutes

Unknowns

The total distance in km

Constraints

30 minutes is half of one hour, so the time is 2 and a half hours
Distance equals the per-hour amount times the number of hours

2 · Planchoose the strategy

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

Distance is a rate problem: km-per-hour times hours gives km. Tracking the unit 'km in one hour' as the per-unit amount and recognizing 30 minutes as half an hour lets us split the trip into 2 full hours plus a half hour.

3 · Execute3 carry out the plan

1Distance in the 2 whole hours

#7 Identify Subproblems 4.NBT.B.5

Each hour adds 916 km, so 2 hours add 916 x 2 = 1832 km.

916 \times 2 = 1832 \text{ km}

2 equal hours is just multiplying the one-hour distance by 2.

2Distance in the extra 30 minutes

#8 Analyze the Units 4.OA.A.2

30 minutes is half an hour, so the plane covers half of 916 km, which is 916 / 2 = 458 km.

916 \div 2 = 458 \text{ km}

Half an hour means half the hourly distance -- a simple halving.

3Add the two parts

#7 Identify Subproblems 4.OA.A.3

Total distance is the 2-hour part plus the half-hour part: 1832 + 458 = 2290 km.

1832 + 458 = 2290 \text{ km}

Adding the whole-hour and half-hour distances gives the full trip.

Answer: 2290 km

4 · Reviewdoes it hold up?

In 2 and a half hours the distance should be a bit more than 2 x 916 = 1832 and less than 3 x 916 = 2748. The answer 2290 falls between them, as expected. Units stay in km throughout.

Another way: Convert to half-hours: 2 h 30 min is 5 half-hours, and each half-hour covers 458 km, so 458 x 5 = 2290 km, the same result.

Standardsmin grade 4

4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison — Using the per-hour distance as the unit amount and scaling it to find the half-hour distance.
4.OA.A.3 Solve multi-step word problems using four operations with whole numbers — Combining the whole-hour and half-hour distances into the total.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Computing 916 x 2 for the whole hours.

💡Takeaway. This only needs Grade 4 multiplying and halving -- 2 full hours plus a half hour of the same speed!

How many times the unit quantity · 10 practice problems

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