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Slope of a time-distance line graph is speed · 8 practice problems

4.MD.A.25.MD.B.2

Generated variants — 8

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

Variant 1 answer: 45 minutes

The line graph shows the relationship between time and distance for Noah riding a bike to the school that is $3$ km away. Find how many minutes Noah spent actually moving on the bike.

The graph is titled "Distance from Home." The horizontal axis is time: the major mark $1$ stands for $1$ hour, and $1$ hour is divided into $4$ small squares, so each small square is $15$ minutes. The vertical axis is distance from home in kilometers (km): $0$ , $1$ , $2$ , $3$ . Starting from $(0$ min, $0$ km $)$ , the line rises from $0$ km to $1$ km over $1$ square, then stays flat at $1$ km for $2$ squares, then rises from $1$ km to $2$ km over $1$ square, then stays flat at $2$ km for $1$ square, then rises from $2$ km to $3$ km over $1$ square. (Sloped segments are where Noah was riding; flat segments are where the bike had stopped.)

Show solution

Understand

A time-distance line graph shows Noah biking a total of 3 km. Each small square is 15 minutes. Sloped (rising) parts are riding; flat parts are stopped. I must find how many minutes Noah spent actually moving.

Givens

Each small grid square = 15 minutes
Sloped (rising) segments mean moving; flat segments mean stopped
Rising segments: 0 to 1 km over 1 square(s); 1 to 2 km over 1 square(s); 2 to 3 km over 1 square(s)
Flat (stopped) squares total 3

Unknowns

Total minutes Noah spent moving on the bike

Constraints

Only the sloped segments count as moving time

Plan

#1 Draw a Diagram · also uses: #8 Analyze the Units

I read the graph to separate sloped (moving) squares from flat (stopped) squares, count only the sloped squares, then convert squares to minutes using one square = 15 minutes.

Execute

#1 Draw a Diagram 5.MD.B.2

The sloped (rising) parts cover 1 + 1 + 1 = 3 squares of moving. The flat parts (3 squares) are stops and do not count.

1 + 1 + 1 = 3 \text{ squares moving}

A rising line means distance is changing, so the rider is moving only there.

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

Each square is 15 minutes, so 3 moving squares = 3 x 15 = 45 minutes.

3 \times 15 = 45 \text{ minutes}

Multiplying square-count by minutes-per-square gives total moving time.

Answer: 45 minutes

Review

There are 6 squares of graph time total (3 sloped + 3 flat) = 90 minutes for the whole trip; the moving part is 3 squares = 45 minutes, which is less than the full trip and sensible.

Work it as a subproblem total (tool 7): the whole trip is 90 minutes, stopped time is the 3 flat squares = 45 minutes, so moving = 90 - 45 = 45 minutes - the same answer.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the graph to tell moving (sloped) from stopped (flat) segments
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Converting grid squares to minutes of moving time

💡 On a time-distance graph the slanted parts are when you're moving - count those squares and turn them into minutes!

Variant 2 answer: 60 minutes

The line graph shows the relationship between time and distance for Ava riding a bike to her grandma's house that is $5$ km away. Find how many minutes Ava spent actually moving on the bike.

The graph is titled "Distance from Home." The horizontal axis is time: the major mark $1$ stands for $1$ hour, and $1$ hour is divided into $4$ small squares, so each small square is $15$ minutes. The vertical axis is distance from home in kilometers (km): $0$ , $1$ , $2$ , $3$ , $4$ , $5$ . Starting from $(0$ min, $0$ km $)$ , the line rises from $0$ km to $2$ km over $1$ square, then stays flat at $2$ km for $3$ squares, then rises from $2$ km to $3$ km over $1$ square, then stays flat at $3$ km for $1$ square, then rises from $3$ km to $5$ km over $2$ squares. (Sloped segments are where Ava was riding; flat segments are where the bike had stopped.)

Show solution

Understand

A time-distance line graph shows Ava biking a total of 5 km. Each small square is 15 minutes. Sloped (rising) parts are riding; flat parts are stopped. I must find how many minutes Ava spent actually moving.

Givens

Each small grid square = 15 minutes
Sloped (rising) segments mean moving; flat segments mean stopped
Rising segments: 0 to 2 km over 1 square(s); 2 to 3 km over 1 square(s); 3 to 5 km over 2 square(s)
Flat (stopped) squares total 4

Unknowns

Total minutes Ava spent moving on the bike

Constraints

Only the sloped segments count as moving time

Plan

#1 Draw a Diagram · also uses: #8 Analyze the Units

I read the graph to separate sloped (moving) squares from flat (stopped) squares, count only the sloped squares, then convert squares to minutes using one square = 15 minutes.

Execute

#1 Draw a Diagram 5.MD.B.2

The sloped (rising) parts cover 1 + 1 + 2 = 4 squares of moving. The flat parts (4 squares) are stops and do not count.

1 + 1 + 2 = 4 \text{ squares moving}

A rising line means distance is changing, so the rider is moving only there.

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

Each square is 15 minutes, so 4 moving squares = 4 x 15 = 60 minutes.

4 \times 15 = 60 \text{ minutes}

Multiplying square-count by minutes-per-square gives total moving time.

Answer: 60 minutes

Review

There are 8 squares of graph time total (4 sloped + 4 flat) = 120 minutes for the whole trip; the moving part is 4 squares = 60 minutes, which is less than the full trip and sensible.

Work it as a subproblem total (tool 7): the whole trip is 120 minutes, stopped time is the 4 flat squares = 60 minutes, so moving = 120 - 60 = 60 minutes - the same answer.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the graph to tell moving (sloped) from stopped (flat) segments
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Converting grid squares to minutes of moving time

💡 On a time-distance graph the slanted parts are when you're moving - count those squares and turn them into minutes!

Variant 3 answer: 60 minutes

The line graph shows the relationship between time and distance for Leo riding a bike to the park that is $4$ km away. Find how many minutes Leo spent actually moving on the bike.

The graph is titled "Distance from Home." The horizontal axis is time: the major mark $1$ stands for $1$ hour, and $1$ hour is divided into $4$ small squares, so each small square is $15$ minutes. The vertical axis is distance from home in kilometers (km): $0$ , $1$ , $2$ , $3$ , $4$ . Starting from $(0$ min, $0$ km $)$ , the line rises from $0$ km to $2$ km over $2$ squares, then stays flat at $2$ km for $1$ square, then rises from $2$ km to $3$ km over $1$ square, then stays flat at $3$ km for $1$ square, then rises from $3$ km to $4$ km over $1$ square. (Sloped segments are where Leo was riding; flat segments are where the bike had stopped.)

Show solution

Understand

A time-distance line graph shows Leo biking a total of 4 km. Each small square is 15 minutes. Sloped (rising) parts are riding; flat parts are stopped. I must find how many minutes Leo spent actually moving.

Givens

Each small grid square = 15 minutes
Sloped (rising) segments mean moving; flat segments mean stopped
Rising segments: 0 to 2 km over 2 square(s); 2 to 3 km over 1 square(s); 3 to 4 km over 1 square(s)
Flat (stopped) squares total 2

Unknowns

Total minutes Leo spent moving on the bike

Constraints

Only the sloped segments count as moving time

Plan

#1 Draw a Diagram · also uses: #8 Analyze the Units

I read the graph to separate sloped (moving) squares from flat (stopped) squares, count only the sloped squares, then convert squares to minutes using one square = 15 minutes.

Execute

#1 Draw a Diagram 5.MD.B.2

The sloped (rising) parts cover 2 + 1 + 1 = 4 squares of moving. The flat parts (2 squares) are stops and do not count.

2 + 1 + 1 = 4 \text{ squares moving}

A rising line means distance is changing, so the rider is moving only there.

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

Each square is 15 minutes, so 4 moving squares = 4 x 15 = 60 minutes.

4 \times 15 = 60 \text{ minutes}

Multiplying square-count by minutes-per-square gives total moving time.

Answer: 60 minutes

Review

There are 6 squares of graph time total (4 sloped + 2 flat) = 90 minutes for the whole trip; the moving part is 4 squares = 60 minutes, which is less than the full trip and sensible.

Work it as a subproblem total (tool 7): the whole trip is 90 minutes, stopped time is the 2 flat squares = 30 minutes, so moving = 90 - 30 = 60 minutes - the same answer.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the graph to tell moving (sloped) from stopped (flat) segments
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Converting grid squares to minutes of moving time

💡 On a time-distance graph the slanted parts are when you're moving - count those squares and turn them into minutes!

Variant 4 answer: 45 minutes

The line graph shows the relationship between time and distance for Ruby riding a bike to the museum that is $4$ km away. Find how many minutes Ruby spent actually moving on the bike.

The graph is titled "Distance from Home." The horizontal axis is time: the major mark $1$ stands for $1$ hour, and $1$ hour is divided into $4$ small squares, so each small square is $15$ minutes. The vertical axis is distance from home in kilometers (km): $0$ , $1$ , $2$ , $3$ , $4$ . Starting from $(0$ min, $0$ km $)$ , the line rises from $0$ km to $3$ km over $2$ squares, then stays flat at $3$ km for $1$ square, then rises from $3$ km to $4$ km over $1$ square, then stays flat at $4$ km for $2$ squares. (Sloped segments are where Ruby was riding; flat segments are where the bike had stopped.)

Show solution

Understand

A time-distance line graph shows Ruby biking a total of 4 km. Each small square is 15 minutes. Sloped (rising) parts are riding; flat parts are stopped. I must find how many minutes Ruby spent actually moving.

Givens

Each small grid square = 15 minutes
Sloped (rising) segments mean moving; flat segments mean stopped
Rising segments: 0 to 3 km over 2 square(s); 3 to 4 km over 1 square(s)
Flat (stopped) squares total 3

Unknowns

Total minutes Ruby spent moving on the bike

Constraints

Only the sloped segments count as moving time

Plan

#1 Draw a Diagram · also uses: #8 Analyze the Units

I read the graph to separate sloped (moving) squares from flat (stopped) squares, count only the sloped squares, then convert squares to minutes using one square = 15 minutes.

Execute

#1 Draw a Diagram 5.MD.B.2

The sloped (rising) parts cover 2 + 1 = 3 squares of moving. The flat parts (3 squares) are stops and do not count.

2 + 1 = 3 \text{ squares moving}

A rising line means distance is changing, so the rider is moving only there.

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

Each square is 15 minutes, so 3 moving squares = 3 x 15 = 45 minutes.

3 \times 15 = 45 \text{ minutes}

Multiplying square-count by minutes-per-square gives total moving time.

Answer: 45 minutes

Review

There are 6 squares of graph time total (3 sloped + 3 flat) = 90 minutes for the whole trip; the moving part is 3 squares = 45 minutes, which is less than the full trip and sensible.

Work it as a subproblem total (tool 7): the whole trip is 90 minutes, stopped time is the 3 flat squares = 45 minutes, so moving = 90 - 45 = 45 minutes - the same answer.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the graph to tell moving (sloped) from stopped (flat) segments
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Converting grid squares to minutes of moving time

💡 On a time-distance graph the slanted parts are when you're moving - count those squares and turn them into minutes!

Variant 5 answer: 60 minutes

The line graph shows the relationship between time and distance for Sam riding a bike to the pool that is $4$ km away. Find how many minutes Sam spent actually moving on the bike.

The graph is titled "Distance from Home." The horizontal axis is time: the major mark $1$ stands for $1$ hour, and $1$ hour is divided into $4$ small squares, so each small square is $15$ minutes. The vertical axis is distance from home in kilometers (km): $0$ , $1$ , $2$ , $3$ , $4$ . Starting from $(0$ min, $0$ km $)$ , the line rises from $0$ km to $1$ km over $1$ square, then stays flat at $1$ km for $1$ square, then rises from $1$ km to $2$ km over $1$ square, then stays flat at $2$ km for $1$ square, then rises from $2$ km to $4$ km over $2$ squares. (Sloped segments are where Sam was riding; flat segments are where the bike had stopped.)

Show solution

Understand

A time-distance line graph shows Sam biking a total of 4 km. Each small square is 15 minutes. Sloped (rising) parts are riding; flat parts are stopped. I must find how many minutes Sam spent actually moving.

Givens

Each small grid square = 15 minutes
Sloped (rising) segments mean moving; flat segments mean stopped
Rising segments: 0 to 1 km over 1 square(s); 1 to 2 km over 1 square(s); 2 to 4 km over 2 square(s)
Flat (stopped) squares total 2

Unknowns

Total minutes Sam spent moving on the bike

Constraints

Only the sloped segments count as moving time

Plan

#1 Draw a Diagram · also uses: #8 Analyze the Units

I read the graph to separate sloped (moving) squares from flat (stopped) squares, count only the sloped squares, then convert squares to minutes using one square = 15 minutes.

Execute

#1 Draw a Diagram 5.MD.B.2

The sloped (rising) parts cover 1 + 1 + 2 = 4 squares of moving. The flat parts (2 squares) are stops and do not count.

1 + 1 + 2 = 4 \text{ squares moving}

A rising line means distance is changing, so the rider is moving only there.

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

Each square is 15 minutes, so 4 moving squares = 4 x 15 = 60 minutes.

4 \times 15 = 60 \text{ minutes}

Multiplying square-count by minutes-per-square gives total moving time.

Answer: 60 minutes

Review

There are 6 squares of graph time total (4 sloped + 2 flat) = 90 minutes for the whole trip; the moving part is 4 squares = 60 minutes, which is less than the full trip and sensible.

Work it as a subproblem total (tool 7): the whole trip is 90 minutes, stopped time is the 2 flat squares = 30 minutes, so moving = 90 - 30 = 60 minutes - the same answer.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the graph to tell moving (sloped) from stopped (flat) segments
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Converting grid squares to minutes of moving time

💡 On a time-distance graph the slanted parts are when you're moving - count those squares and turn them into minutes!

Variant 6 answer: 60 minutes

The line graph shows the relationship between time and distance for Ivy riding a bike to the market that is $4$ km away. Find how many minutes Ivy spent actually moving on the bike.

The graph is titled "Distance from Home." The horizontal axis is time: the major mark $1$ stands for $1$ hour, and $1$ hour is divided into $4$ small squares, so each small square is $15$ minutes. The vertical axis is distance from home in kilometers (km): $0$ , $1$ , $2$ , $3$ , $4$ . Starting from $(0$ min, $0$ km $)$ , the line rises from $0$ km to $2$ km over $1$ square, then stays flat at $2$ km for $1$ square, then rises from $2$ km to $3$ km over $2$ squares, then stays flat at $3$ km for $1$ square, then rises from $3$ km to $4$ km over $1$ square. (Sloped segments are where Ivy was riding; flat segments are where the bike had stopped.)

Show solution

Understand

A time-distance line graph shows Ivy biking a total of 4 km. Each small square is 15 minutes. Sloped (rising) parts are riding; flat parts are stopped. I must find how many minutes Ivy spent actually moving.

Givens

Each small grid square = 15 minutes
Sloped (rising) segments mean moving; flat segments mean stopped
Rising segments: 0 to 2 km over 1 square(s); 2 to 3 km over 2 square(s); 3 to 4 km over 1 square(s)
Flat (stopped) squares total 2

Unknowns

Total minutes Ivy spent moving on the bike

Constraints

Only the sloped segments count as moving time

Plan

#1 Draw a Diagram · also uses: #8 Analyze the Units

I read the graph to separate sloped (moving) squares from flat (stopped) squares, count only the sloped squares, then convert squares to minutes using one square = 15 minutes.

Execute

#1 Draw a Diagram 5.MD.B.2

The sloped (rising) parts cover 1 + 2 + 1 = 4 squares of moving. The flat parts (2 squares) are stops and do not count.

1 + 2 + 1 = 4 \text{ squares moving}

A rising line means distance is changing, so the rider is moving only there.

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

Each square is 15 minutes, so 4 moving squares = 4 x 15 = 60 minutes.

4 \times 15 = 60 \text{ minutes}

Multiplying square-count by minutes-per-square gives total moving time.

Answer: 60 minutes

Review

There are 6 squares of graph time total (4 sloped + 2 flat) = 90 minutes for the whole trip; the moving part is 4 squares = 60 minutes, which is less than the full trip and sensible.

Work it as a subproblem total (tool 7): the whole trip is 90 minutes, stopped time is the 2 flat squares = 30 minutes, so moving = 90 - 30 = 60 minutes - the same answer.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the graph to tell moving (sloped) from stopped (flat) segments
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Converting grid squares to minutes of moving time

💡 On a time-distance graph the slanted parts are when you're moving - count those squares and turn them into minutes!

Variant 7 answer: 60 minutes

The line graph shows the relationship between time and distance for Mia riding a bike to the library that is $4$ km away. Find how many minutes Mia spent actually moving on the bike.

The graph is titled "Distance from Home." The horizontal axis is time: the major mark $1$ stands for $1$ hour, and $1$ hour is divided into $4$ small squares, so each small square is $15$ minutes. The vertical axis is distance from home in kilometers (km): $0$ , $1$ , $2$ , $3$ , $4$ . Starting from $(0$ min, $0$ km $)$ , the line rises from $0$ km to $1$ km over $1$ square, then stays flat at $1$ km for $1$ square, then rises from $1$ km to $3$ km over $2$ squares, then stays flat at $3$ km for $2$ squares, then rises from $3$ km to $4$ km over $1$ square. (Sloped segments are where Mia was riding; flat segments are where the bike had stopped.)

Show solution

Understand

A time-distance line graph shows Mia biking a total of 4 km. Each small square is 15 minutes. Sloped (rising) parts are riding; flat parts are stopped. I must find how many minutes Mia spent actually moving.

Givens

Each small grid square = 15 minutes
Sloped (rising) segments mean moving; flat segments mean stopped
Rising segments: 0 to 1 km over 1 square(s); 1 to 3 km over 2 square(s); 3 to 4 km over 1 square(s)
Flat (stopped) squares total 3

Unknowns

Total minutes Mia spent moving on the bike

Constraints

Only the sloped segments count as moving time

Plan

#1 Draw a Diagram · also uses: #8 Analyze the Units

I read the graph to separate sloped (moving) squares from flat (stopped) squares, count only the sloped squares, then convert squares to minutes using one square = 15 minutes.

Execute

#1 Draw a Diagram 5.MD.B.2

The sloped (rising) parts cover 1 + 2 + 1 = 4 squares of moving. The flat parts (3 squares) are stops and do not count.

1 + 2 + 1 = 4 \text{ squares moving}

A rising line means distance is changing, so the rider is moving only there.

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

Each square is 15 minutes, so 4 moving squares = 4 x 15 = 60 minutes.

4 \times 15 = 60 \text{ minutes}

Multiplying square-count by minutes-per-square gives total moving time.

Answer: 60 minutes

Review

There are 7 squares of graph time total (4 sloped + 3 flat) = 105 minutes for the whole trip; the moving part is 4 squares = 60 minutes, which is less than the full trip and sensible.

Work it as a subproblem total (tool 7): the whole trip is 105 minutes, stopped time is the 3 flat squares = 45 minutes, so moving = 105 - 45 = 60 minutes - the same answer.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the graph to tell moving (sloped) from stopped (flat) segments
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Converting grid squares to minutes of moving time

💡 On a time-distance graph the slanted parts are when you're moving - count those squares and turn them into minutes!

Variant 8 answer: 45 minutes

The line graph shows the relationship between time and distance for Owen riding a bike to a friend's house that is $4$ km away. Find how many minutes Owen spent actually moving on the bike.

The graph is titled "Distance from Home." The horizontal axis is time: the major mark $1$ stands for $1$ hour, and $1$ hour is divided into $4$ small squares, so each small square is $15$ minutes. The vertical axis is distance from home in kilometers (km): $0$ , $1$ , $2$ , $3$ , $4$ . Starting from $(0$ min, $0$ km $)$ , the line rises from $0$ km to $2$ km over $1$ square, then stays flat at $2$ km for $2$ squares, then rises from $2$ km to $3$ km over $1$ square, then stays flat at $3$ km for $1$ square, then rises from $3$ km to $4$ km over $1$ square. (Sloped segments are where Owen was riding; flat segments are where the bike had stopped.)

Show solution

Understand

A time-distance line graph shows Owen biking a total of 4 km. Each small square is 15 minutes. Sloped (rising) parts are riding; flat parts are stopped. I must find how many minutes Owen spent actually moving.

Givens

Each small grid square = 15 minutes
Sloped (rising) segments mean moving; flat segments mean stopped
Rising segments: 0 to 2 km over 1 square(s); 2 to 3 km over 1 square(s); 3 to 4 km over 1 square(s)
Flat (stopped) squares total 3

Unknowns

Total minutes Owen spent moving on the bike

Constraints

Only the sloped segments count as moving time

Plan

#1 Draw a Diagram · also uses: #8 Analyze the Units

I read the graph to separate sloped (moving) squares from flat (stopped) squares, count only the sloped squares, then convert squares to minutes using one square = 15 minutes.

Execute

#1 Draw a Diagram 5.MD.B.2

The sloped (rising) parts cover 1 + 1 + 1 = 3 squares of moving. The flat parts (3 squares) are stops and do not count.

1 + 1 + 1 = 3 \text{ squares moving}

A rising line means distance is changing, so the rider is moving only there.

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

Each square is 15 minutes, so 3 moving squares = 3 x 15 = 45 minutes.

3 \times 15 = 45 \text{ minutes}

Multiplying square-count by minutes-per-square gives total moving time.

Answer: 45 minutes

Review

There are 6 squares of graph time total (3 sloped + 3 flat) = 90 minutes for the whole trip; the moving part is 3 squares = 45 minutes, which is less than the full trip and sensible.

Work it as a subproblem total (tool 7): the whole trip is 90 minutes, stopped time is the 3 flat squares = 45 minutes, so moving = 90 - 45 = 45 minutes - the same answer.

Standards · min grade 5

5.MD.B.2 Make a line plot to display a data set and solve problems using the data — Reading the graph to tell moving (sloped) from stopped (flat) segments
4.MD.A.2 Solve word problems involving distances, time, liquid volumes, and money — Converting grid squares to minutes of moving time

💡 On a time-distance graph the slanted parts are when you're moving - count those squares and turn them into minutes!