Worksheet

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:

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

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

A

B

C

D

2

Explain why the following travel graph does not make sense:

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

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?

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?

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?

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?

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?

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.

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?

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?

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.

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?

14

Consider the following travel graph:

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.

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?

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?

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.

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.

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.

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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creates and displays number patterns; graphs and analyses linear relationships; and performs transformations on the Cartesian plane

performs calculations of time that involve mixed units, and interprets time zones