KS3 Maths · Year 8 · Chapter 12: Compound units · Lesson 1

Speed

Year 8About 75 minutesCalculator allowed51 marks

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Date

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Quick questions to start.

A1
Needed today
Write $45$ minutes as a decimal of an hour.
[1 mark]
Answer
A2
Needed today
Change $2.7$ km into metres.
[1 mark]
Answer
A3
Last lesson
Work out the value of $x^{3} - 2 x$ when $x = 3$ .
[1 mark]
Answer
A4
Year 7
$8$ pens cost £ $6$ . Work out the cost of $12$ pens.
[1 mark]
Answer

Example, then your turn

Year 8

Speed $=$ distance $\div$ time. Your teacher works through each example with you. Then try the one beside it.

Example 1

A cyclist rides $54$ km in $3$ hours. Work out her average speed.

Hint Speed

=

distance

\div

time. Kilometres and hours give km/h.

B1
A train travels $225$ km in $2.5$ hours. Work out its average speed.
[2 marks]
Answer $\dots$ km/h

Example 2

A bus travels $21$ km in $35$ minutes. Work out its average speed in km/h.

Hint Change the time to hours first: divide the minutes by

60

B2
A car travels $66$ km in $1$ hour $12$ minutes. Work out its average speed in km/h.
[3 marks]
Answer $\dots$ km/h

Example 3

A boat sails at $14$ km/h for $2$ hours $15$ minutes. How far does it sail?

Hint Distance

=

speed

\times

time.

15

minutes is

0.25

of an hour.

B3
Zara walks at $4.8$ km/h for $1$ hour $40$ minutes. How far does she walk?
[3 marks]
Answer $\dots$ km

Example 4

A coach travels $130$ km at an average speed of $60$ km/h. How long does the journey take? Give your answer in hours and minutes.

Hint Time

=

distance

\div

speed. Then change the decimal part of the hours into minutes.

B4
A van travels $99$ km at an average speed of $54$ km/h. How long does the journey take? Give your answer in hours and minutes.
[3 marks]
Answer $\dots$ hours $\dots$ minutes

Example 5

Change a speed of $72$ km/h into metres per second.

Hint

1

= 1000

m and

1

hour

= 3600

seconds.

B5
Change a speed of $126$ km/h into metres per second.
[2 marks]
Answer $\dots$ m/s

Practice

Year 8

C1
A cheetah can run at $28$ m/s. Change this speed into km/h.
[2 marks]
Answer $\dots$ km/h
C2
The graph shows Ben's bike ride. Work out his speed, in km/h, for the first $30$ minutes and for the last $15$ minutes.
[3 marks]

C3
Ella runs $1800$ m in $8$ minutes. Ravi runs at $14$ km/h. Who runs faster? Show how you decide.
[3 marks]
C4
A drone flies at $12.5$ m/s. How long does it take to fly $1$ km? Give your answer in minutes and seconds.
[2 marks]
Answer $\dots$ minutes $\dots$ seconds
C5
A journey is $240$ km long. Work out the missing times in the table.
[3 marks]
C6
A plane flies at $840$ km/h. How far does it fly in one minute?
[2 marks]
Answer $\dots$ km

Exam-style questions

GCSE Foundation

D1
Ali drives $60$ km at $30$ km/h. Then he drives another $60$ km at $60$ km/h. He says: "My average speed for the whole journey is $45$ km/h, because $(30 + 60) \div 2 = 45$ ."
Show that Ali is wrong. Work out his average speed for the whole journey.
[3 marks]

D2
A train leaves Leeds at 09:45 and arrives in London at 12:05. The journey is $287$ km. Work out the average speed of the train in km/h.
[4 marks]
Answer $\dots$ km/h
D3
Mia cycles $18$ km from her home to her gran's house at an average speed of $15$ km/h.
(a)
How many minutes does the ride take?
[2 marks]
Answer $\dots$ minutes
(b)
Mia leaves home at 13:50. She stays at her gran's for $2$ hours $15$ minutes. She cycles home along the same road at $12$ km/h. At what time does she get home?
[3 marks]
Answer
Total for D3: 5 marks
D4
A car travels $500$ m in $25$ seconds. The speed limit on the road is $70$ km/h. Is the car going faster than the speed limit? You must show your working.
[4 marks]

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
Sam leaves home at 10:00 and walks along a path at $5$ km/h. Tom leaves the same home at 10:30 and cycles along the same path at $15$ km/h. At what time does Tom catch up with Sam?
[3 marks]
Hint 1 · What to try
At 10:30 Sam has already walked $5 \times 0.5$ km.
Hint 2 · The first line
Each hour Tom closes the gap by $15 - 5 = 10$ km.
Hint 3 · The full method
The gap is $2.5$ km. $2.5 \div 10 = 0.25$ hours $= 15$ minutes after 10:30.
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can work out a speed, a distance or a time.
I can work with times in hours and minutes.
I can change a speed between km/h and m/s.
I can read a speed from a distance-time graph.

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