Question

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

Explanation: Speed is distance an object travelled per unit time.

It is represented by letter v and can assume various units.

1)
`v=(distance)/(time)=(d)/(t)`

`v=(90)/(5)`

v = 18 miles per hour

Her average speed is 18 mph.

2) Rearraging formula for distance:

d = v.t

d = 70 * 4

d = 280 miles

You would travel 280 miles.

3)
`v=(d)/(t)`

`v=(315)/(6)`

v = 52.5 mph

My average speed is 52.5 mph.

4) Rearranging formula to determine time:

`t=(d)/(v)`

`t=(210)/(90)`

t = 2.34 hours

It will take 2 hours and half to arrive in Leeds. So, we will be expected to arrive at 12:04.

5) The unit change but the way of calculating time is the same.

`t=(2000)/(4)`

t = 500 s

or t = 8.34 minutes

It will take, for an athlete to run 2000m, 8.34 minutes.

6) a) All units must match, so for a speed in mph:

45 minutes is 0.75 hours. Total time is 8.75 hours.

`v=(420)/(8.75)`

v = 560 mph

The average speed is 560 mph.

b)
`t=(d)/(v)`

`t=(420)/(63)`

t = 6.67 hours

Sam will take 6.67 hours to covered the distance.