Practice · Minutes are sixtieths of an hour, and a quotient that never ends is rounded · Sensim Math

Variant 1 easy

A car travels $85\ \text{km}$ in $2$ hours $18$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $100\ \text{km}$ in $1$ hour $30$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $105\ \text{km}$ in $1$ hour $48$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $125\ \text{km}$ in $3$ hours $18$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $155\ \text{km}$ in $3$ hours $48$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $160\ \text{km}$ in $1$ hour $48$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $220\ \text{km}$ in $2$ hours $24$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $240\ \text{km}$ in $4$ hours $6$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $285\ \text{km}$ in $2$ hours $18$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $325\ \text{km}$ in $2$ hours $54$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $390\ \text{km}$ in $4$ hours $54$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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

A car travels $410\ \text{km}$ in $3$ hours $54$ minutes. If it keeps a steady speed, how many kilometers does it travel in one hour? Give the answer rounded to one decimal place.

Your answer

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 \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 \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\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.

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

Generated variants — 12

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Givens

Unknowns

Constraints

Where next?