Topics
3. Ratios and Rates
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Middle Years

3.06 Travel graphs

Lesson
Worksheet
Worksheet
Travel graphs
1

The manufacturer of a dishwasher wants to create a graph showing how one of their dishwasher models work. The stages of its operation are given below:

  1. The dishwasher quickly fills to half-way and performs a short wash.
  2. The dishwasher empties completely.
  3. The dishwasher completely fills up quickly and remains full over the course of the wash.
  4. The dishwasher empties completely.

Which of the following graphs match the water level inside the dishwasher throughout a cycle:

A
10
20
30
40
50
\text{Time (mins)}
y
B
10
20
30
40
50
\text{Time (mins)}
y
C
10
20
30
40
50
\text{Time (mins)}
y
D
10
20
30
40
50
\text{Time (mins)}
y
2

Explain why the following travel graph does not make sense:

2\text{ pm}
3\text{ pm}
4\text{ pm}
5\text{ pm}
\text{Time}
1\text{ km}
2\text{ km}
3\text{ km}
4\text{ km}
5\text{ km}
6\text{ km}
\text{Distance}
3

The travel graph shows the first ten minutes of a student's journey home from school:

Describe their travel between the following times:

a

0 to 3 minutes

b

3 to 6 minutes

c

6 to 9 minutes

d

9 to 10 minutes

1
2
3
4
5
6
7
8
9
10
\text{Time (mins)}
1
2
3
4
5
6
7
8
9
10
\text{Distance (km)}
4

Edward walks from his home to school on occasion. The graph represents his distance from school over one particular journey.

a

How far away is Edward's home from his school?

b

How long does Edward take to get to school?

c

How far is Edward from his school after 10 minutes?

d

How long did he have left in his trip when he was 1200 \text{ m} away from his school?

10
20
30
40
50
\text{Time (min)}
250
500
750
1000
1250
1500
1750
2000
2250
\text{Distance (m)}
5

Two siblings, Apollo and Artemis, leave home at different times. They are travelling to see their favourite sports team compete in the championship. The stadium is 30 \,\text{km} away and the match starts at 9:00 pm.

a

At what times did they both leave home?

b

Between which two times were Apollo and Artemis the same distance from home?

c

Who was travelling faster?

d

Did Apollo make it to the stadium on time?

2
3
4
5
6
7
8
9
10
\text{Time (pm)}
5\text{ km}
10\text{ km}
15\text{ km}
20\text{ km}
25\text{ km}
30\text{ km}
\text{Distance}
6

The graph shows the progress of two competitors in a cycling race.

a

Who is travelling faster, Justin or Oliver?

b

How much faster does this person travel?

1
2
3
4
5
6
7
8
\text{Time}
25
50
75
100
125
150
175
200
225
250
\text{Distance}
7

A man and his wife exercise each day for 20 minutes before dinner. The wife walks briskly, while the man runs.

a

Find the difference in distance they cover after 20 minutes.

b

Find the distance the wife covers each minute.

c

Find the distance the husband covers each minute.

d

How long would it take the wife to walk the same distance that her husband runs in 6 minutes?

4
8
12
16
20
24
\text{Time (min)}
400
800
1200
1600
2000
2400
2800
3200
3600
4000
4400
4800
\text{Distance (m)}
8

Two students were walking on a straight walking track, their travel graph is shown:

a

How far did Student A walk?

b

How many more metres did Student A walk than Student B during the first 5 minutes?

c

Find the average speed of Student A in metres per minute.

d

Find the average speed of Student B in metres per minute.

e

Assuming Student A and Student B walk at these speeds to complete the 2 \text{ km} track on the field, how many minutes longer would Student B take than Student A?

1
2
3
4
5
6
\text{Time (min)}
50
100
150
200
250
\text{Distance (m)}
9

The travel graph of John and Kate is shown:

a

How many more hours did John take to travel than Kate?

b

Find John's average speed in km/h for the trip, correct to two decimal places.

c

Find Kate's average speed in km/h for the trip.

d

At what time has they travelled the same distance?

v

Find the distance travelled by this time.

9\text{ am}
10\text{ am}
11\text{ am}
12\text{ am}
\text{Time}
5
10
15
20
25
30
\text{Distance (km)}
10

This travel graph represents a train's journey between the airport and a nearby station:

a

How far did the train travel over the 10 minute period?

b

When was the train travelling the fastest?

1
2
3
4
5
6
7
8
9
10
\text{Time (mins)}
1
2
3
4
5
6
7
8
9
10
\text{Distance (km)}
11

Kenneth works for a delivery company. The following graph shows his distance from the warehouse throughout his shift:

a

How far was Kenneth from the warehouse at the beginning of the time period shown?

b

How far was he from the warehouse after 8 hours?

c

How many times did he visit the warehouse during this time period?

d

Calculate the total distance that he traveled between 1 and 4 hours.

e

When was Kenneth travelling the fastest?

1
2
3
4
5
6
7
8
9
\text{Time (hours)}
1
2
3
4
5
6
7
8
9
\text{Distance (km)}
12

The Weber family travel 600\,\text{km} every year for their annual holidays.

Their distance from home on the trip this year is given in the following travel graph:

a

When did they stop for a break?

b

How far from their destination were they after 2 hours?

c

Identify two time periods when they were travelling at the same speed.

1
2
3
4
5
6
7
8
\text{Time (hours)}
100
200
300
400
500
600
\text{Distance (km)}
13

Castor and Pollux are working on a bushfire prevention team. Over the course of their 10-hour shift they move along a boundary and remove all flammable material they find.

The following travel graph shows their distance from the base throughout their shift:

a

How far from the base was Pollux when the shift began?

b

How far apart were Castor and Pollux after 2 hours?

c

When did Castor and Pollux meet up?

d

When was Pollux travelling the same speed as Castor was traveling at in his first three hours?

1
2
3
4
5
6
7
8
9
10
\text{Time (hours)}
1
2
3
4
5
6
7
8
9
10
\text{Distance (km)}
14

Consider the following travel graph:

8:00
9:00
10:00
11:00
12:00
13:00
14:00
15:00
16:00
17:00
\text{Time}
5
10
15
20
25
30
35
\text{Speed (km/h)}
a

Find the total time taken for the journey.

b

Find the total distance covered in the journey.

c

Find the average speed during the journey, correct to two decimal places.

15

The graph represents Beth's distance from home over a 9 minute interval:

a

When she first started to move, did she travel towards or away from home?

b

For how many minutes did she stay home?

c

How many minutes into her journey was she when she left home?

d

Find Beth's furthest distance from home.

e

How long, from the time she left home, did it take for Beth to return home?

f

Find the total distance she travelled over the 9-minute period.

1
2
3
4
5
6
7
8
9
10
11
\text{Time (min)}
1
2
3
4
5
\text{Distance (km)}
16

The graph shows a traveller's distance from home each hour:

a

At what speed was the person travelling between 11:00 am and 1:00 pm?

b

In which interval of time was the person travelling fastest?

c

What does the horizontal interval on the graph represent?

9
10
11
12
13
14
15
16
17
\text{24-Hour Time}
50
100
150
200
250
300
\text{Distance (km)}
17

This line graph shows the distance Buzz was from his house as he travelled to visit his grandparents:

a

How far was Buzz from his house at 10:30 am?

b

What time did Buzz get back home?

c

What was the furthest distance Buzz was from his house?

10
11
12
13
\text{24-Hour Time}
1
2
3
4
5
\text{Distance (km)}
18

Ben travels forwards and backwards along a straight line. The graph shows Ben's distance from his starting point at various times of the day:

a

How far did Ben travel by 11:00 am?

b

Describe Ben's speed at 11:00 am.

c

Find Ben's speed between 11:00 am and 1:00 pm.

d

Find the distance Ben travelled between 1:00 pm and 2:00 pm.

e

Find the furthest distance travelled from the starting point.

f

Find the total distance travelled by Ben from 9:00 am to 4:00 pm.

9
10
11
12
13
14
15
16
17
\text{24-hour Time}
50
100
150
200
250
300
\text{Distance (km)}
19

Ken starts travelling at 9:00 am from point A and moves towards point B in a straight line.

The distance between Ken and point B at various times in his journey is shown on the graph.

a

How far is point B from point A?

b

How many hours was Ken's journey from point A to point B?

c

Between what time did Ken travel at the fastest speed?

d

Find Ken's fastest speed in km/h.

e

Find the distance in kilometres travelled by Ken between 1:30 pm and 4:00 pm.

f

Find the total distance travelled by Ken from 9:00 am to 4:00 pm.

9
10
11
12
13
14
15
16
17
\text{24-hour Time}
20
40
60
80
100
120
\text{Distance (km)}
20

The following travel graph shows the distance covered by Neil on his journey versus time. Neil took two trips and rested between them.

a

Find the average speed of the first trip.

b

Find the average speed of the second trip.

c

Find the average speed of the entire journey.

2
4
6
8
10
12
14
\text{Time (min)}
2
4
6
8
10
12
14
\text{Distance (km)}
21

Tina is cycling to the bus stop, but halfway there she gets a flat tire and has to push her bike the rest of the way. Upon reaching the bus stop, she has a short wait for the bus and then catches the bus to her final destination.

Construct a travel graph to represent this journey.

22

Paul is driving his child home from school. They travel 6\text{ km} in 10 minutes. After 5 minutes, the car slows down.

Construct a travel graph to represent this journey.

23

A man is driving in a car at a constant speed. After 4 minutes he increases his speed because he is on a highway. The whole drive takes 9 minutes.

Construct a travel graph to represent this journey.

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