Question

SPEED, DISTANCE AND TIME

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1) A cyclist travels a distance of 90 miles in 5 hours. What

was her average speed?

2) How far along a motorway would you travel if you drove at

70 mph for 4 hours?

3) I drive to Bude in Cornwall from Sheffield in about 6

hours. The distance from Sheffield to Bude is 315 miles.

What is my average speed?

4) The distance from Leeds to London is 210 miles. The train

travels at an average speed of 90 mph. If I catch the 9.30 am

train in London, at what time should I expect to arrive in

Leeds?

5) How long will an athlete take to run 2000 m at an average

speed of 4 metres per second?

6) The distance between Sheffield and Land’s End is 420

miles.

a) What is the average speed of a journey from Sheffield to

Land’s End that takes 8 hours 45 minutes?

b) If Sam covered the distance at an average speed of 63

mph, how long would it take him?

Answer 1

1. Speed = 18 miles per hour

2. The distance is 280 miles.

3. The average speed is 52.5 miles per hour.

4. The time to arrive in Leeds would be 11.50 am.

5. Time = 500 s (8 minutes 20 seconds)

6. speed = 48 miles per hour

b. time taken = 6 hours 40 minutes

Explanation:

1. Distance = 90 miles and time = 5 hours

speed =
`(distance)/(time)`

=
`(90)/(5)`

= 18

average speed of the cyclist is 18 miles per hour.

2. speed = 70 mph, and time = 4 hours

speed =
`(distance)/(time)`

distance = speed x time

= 70 x 4

= 280 miles

The distance is 280 miles.

3. distance = 315 miles, and time = 6 hours.

speed =
`(distance)/(time)`

=
`(315)/(6)`

= 52.5

The average speed is 52.5 miles per hour.

4. distance = 210 miles, and speed - 90 mph.

speed =
`(distance)/(time)`

time =
`(distance)/(speed)`

=
`(210)/(90)`

= 2 hours 20 minutes

The time to arrive in Leeds would be 11.50 am.

5. distance = 2000 m, and speed = 4 m/s.

time =
`(distance)/(speed)`

=
`(2000)/(4)`

= 500 s

It would take the athlete 500 s (8 minutes 20 seconds) to cover the distance in the given speed.

6. distance = 420 miles, and time = 8 hours 45 minutes

But, 8 hours 45 minutes = 8
`(3)/(4)` hours.

speed =
`(distance)/(time)`

=
`(420)/(8(3)/(4) )`

= 420 ÷
`(35)/(4)`

= 420 x
`(4)/(35)`

speed = 48 miles per hour

(b) distance = 420 miles, speed = 63 mph.

time =
`(distance)/(speed)`

=
`(420)/(63)`

= 6 hours 40 minutes

time taken = 6 hours 40 minutes