Practice · The decimal part of an hour is not minutes until it is multiplied by 60 · Sensim Math

Variant 1 easy

The distance from Jeju to Ulsan is $108\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $48$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 2 easy

The distance from Jeju to Ulsan is $120\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $80$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 3 easy

The distance from Jeju to Ulsan is $198\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $72$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 4 easy

The distance from Jeju to Ulsan is $225\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $90$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 5 medium

The distance from Jeju to Ulsan is $234\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $72$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 6 medium

The distance from Jeju to Ulsan is $285\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $60$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 7 medium

The distance from Jeju to Ulsan is $324\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $144$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 8 medium

The distance from Jeju to Ulsan is $410\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $40$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A typhoon moves 40 km every hour and has 410 km to cover. We want the time in hours and minutes.

Givens

The distance is 410 km.
The typhoon covers 40 km per hour.

Unknowns

The travel time, in hours and minutes.

Constraints

The speed is steady the whole way.

2 · Planchoose the strategy

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

Dividing gives the time in hours, but the answer is wanted in hours and minutes. The digits after the point are a fraction of an hour, not a number of minutes, so they have to be converted before they are read.

3 · Execute3 carry out the plan

1Divide distance by speed

#7 Identify Subproblems 6.RP.A.2

How many lots of 40 km fit into 410 km.

410 \div 40 = 10.25

10.25 hours.

2Split off the whole hours

#8 Analyze the Units 6.RP.A.3

10 full hours, with 0.25 of an hour left over.

10.25 = 10 + 0.25

The leftover is part of an hour.

3Turn the leftover into minutes

#8 Analyze the Units 6.RP.A.3

An hour is 60 minutes, so multiply the fractional part by 60. Reading it off as minutes directly would be wrong.

0.25 \times 60 = 15

15 minutes.

Answer: 10 hours 15 minutes

4 · Reviewdoes it hold up?

Going back the other way: 10 hours at 40 km is 400 km, and 15 minutes covers the remaining 10 km.

Another way: Reading the digits after the point straight off as minutes is the usual slip. It would name a time that is not 15 minutes past 10 o'clock at all, because those digits count hundredths of an hour, not minutes.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Using kilometres per hour as a unit rate to get a time.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting the fractional hour into minutes.

💡Takeaway. Point two five of an hour is not twenty-five minutes. It is a quarter of sixty.

Variant 9 hard

The distance from Jeju to Ulsan is $492\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $48$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A typhoon moves 48 km every hour and has 492 km to cover. We want the time in hours and minutes.

Givens

The distance is 492 km.
The typhoon covers 48 km per hour.

Unknowns

The travel time, in hours and minutes.

Constraints

The speed is steady the whole way.

2 · Planchoose the strategy

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

Dividing gives the time in hours, but the answer is wanted in hours and minutes. The digits after the point are a fraction of an hour, not a number of minutes, so they have to be converted before they are read.

3 · Execute3 carry out the plan

1Divide distance by speed

#7 Identify Subproblems 6.RP.A.2

How many lots of 48 km fit into 492 km.

492 \div 48 = 10.25

10.25 hours.

2Split off the whole hours

#8 Analyze the Units 6.RP.A.3

10 full hours, with 0.25 of an hour left over.

10.25 = 10 + 0.25

The leftover is part of an hour.

3Turn the leftover into minutes

#8 Analyze the Units 6.RP.A.3

An hour is 60 minutes, so multiply the fractional part by 60. Reading it off as minutes directly would be wrong.

0.25 \times 60 = 15

15 minutes.

Answer: 10 hours 15 minutes

4 · Reviewdoes it hold up?

Going back the other way: 10 hours at 48 km is 480 km, and 15 minutes covers the remaining 12 km.

Another way: Reading the digits after the point straight off as minutes is the usual slip. It would name a time that is not 15 minutes past 10 o'clock at all, because those digits count hundredths of an hour, not minutes.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Using kilometres per hour as a unit rate to get a time.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting the fractional hour into minutes.

💡Takeaway. Point two five of an hour is not twenty-five minutes. It is a quarter of sixty.

Variant 10 hard

The distance from Jeju to Ulsan is $675\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $108$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 11 hard

The distance from Jeju to Ulsan is $837\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $108$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Variant 12 hard

The distance from Jeju to Ulsan is $1890\ \text{km}$ . A typhoon travelling from Jeju toward Ulsan covers distance (in $\text{km}$ ) at a rate of $168$ per hour. How many hours and minutes does it take to go from Jeju to Ulsan?

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A typhoon moves 168 km every hour and has 1890 km to cover. We want the time in hours and minutes.

Givens

The distance is 1890 km.
The typhoon covers 168 km per hour.

Unknowns

The travel time, in hours and minutes.

Constraints

The speed is steady the whole way.

2 · Planchoose the strategy

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

Dividing gives the time in hours, but the answer is wanted in hours and minutes. The digits after the point are a fraction of an hour, not a number of minutes, so they have to be converted before they are read.

3 · Execute3 carry out the plan

1Divide distance by speed

#7 Identify Subproblems 6.RP.A.2

How many lots of 168 km fit into 1890 km.

1890 \div 168 = 11.25

11.25 hours.

2Split off the whole hours

#8 Analyze the Units 6.RP.A.3

11 full hours, with 0.25 of an hour left over.

11.25 = 11 + 0.25

The leftover is part of an hour.

3Turn the leftover into minutes

#8 Analyze the Units 6.RP.A.3

An hour is 60 minutes, so multiply the fractional part by 60. Reading it off as minutes directly would be wrong.

0.25 \times 60 = 15

15 minutes.

Answer: 11 hours 15 minutes

4 · Reviewdoes it hold up?

Going back the other way: 11 hours at 168 km is 1848 km, and 15 minutes covers the remaining 42 km.

Another way: Reading the digits after the point straight off as minutes is the usual slip. It would name a time that is not 15 minutes past 11 o'clock at all, because those digits count hundredths of an hour, not minutes.

Standardsmin grade 6

6.RP.A.2 Understand unit rate a/b associated with a ratio — Using kilometres per hour as a unit rate to get a time.
6.RP.A.3 Use ratio and rate reasoning to solve problems — Converting the fractional hour into minutes.

💡Takeaway. Point two five of an hour is not twenty-five minutes. It is a quarter of sixty.

The decimal part of an hour is not minutes until it is multiplied by 60 · 12 practice problems

Generated variants — 12

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