# 1.5 Speeds

Speed is the ratio of distance travelled to time taken. A runner's speed may be quoted in metres per second, miles per hour or kilometres per hour. The units are given as:

unit of distance *per* unit of time.

When you have a distance covered (such as a mile) and a time taken (such as four minutes) the average speed is defined as

The formula for average speed applies even over a journey made up of several stages.

## Example 6

In 1999, Hicham El Guerrouj held the record for running a mile. He covered the distance in just over 3 minutes 43 seconds. In the same year he also held the world record for the 1500 m race. He completed this distance in 3 minutes 26 seconds.

Work out:

(a) his (average) speed in miles per hour for the 1 mile race;

(b) his (average) speed in kilometres per hour for the 1500 metre race;

(c) compare (a) and (b). In which race was his (average) speed faster assuming that 1.61 km = 1 mile?

### Answer

(a) To find the speed in miles per hour, you need the ratio of the distance in miles to time in hours. In 223 seconds (3 minutes 43 seconds) he ran 1 mile. Therefore in 1 second he would run 1/223 miles. In 3600 seconds (i.e. 1 hour), he would run 3600/223 miles i.e. 16.14 miles (to 2 d.p.). So the athlete's speed is 16.14 miles per hour (to 2 d.p.).

(b) Hicham ran 1500 metres in 3 minutes 26 seconds (i.e. 206 seconds), so he ran metres in 1 second. In 3600 seconds (1 hour) he runs 3600 × metres. That is, 26 213.59 metres per hour. To convert to kilometres: divide by 1000 which gives 26.21 km per hour (to 2 d.p.).

(c) To compare speeds in different units, you need to convert one to the other, say miles per hour to kilometres per hour. Since 1 mile is 1.61 km, 16.14 miles is 16.14 × 1.61 = 25.99 km (to 2 d.p.). Hence 16.14 miles per hour is the same as 25.99 km per hour. This is a lower speed than 26.21 km per hour. So Hicham ran the 1500 metre race faster, which is not surprising as it is a shorter distance.