Just how fast is Usain Bolt? An activity for using maths in science lessons

[Image credit: Daily Telegraph]

This is one of a series of blog posts I've written about numeracy contexts in science teaching.  This one is specifically about converting metric into imperial units, so that we can compare Usain Bolt's speed to the speed of things like cars and other mammals.

It's hard to judge how fast athletes are running, relative to other 'fast' things, because we tend to measure the speed of things like cars in miles per hour whereas athletes run distances measured in metres and timed in minutes or seconds, so we never get any data which allows us to sensibly compare the two.  It's likely children will have no idea how fast a top sprinter (like Usain Bolt) is, compared to a car, or the top speed of familiar mammals like a horse or a cheetah for that matter.  I do recollect a sixth form student in my 'A' level chemistry class once confidently declaring that a top 100m sprinter could be doing around 60 miles per hour, which is well above the actual speed a human can reach using their legs alone.

The way to do the comparison is simply a case of converting between units, but this is not as easy as it sound because miles per hour uses imperial quantities (basically old-fashioned ones, not based on a sensible decimal system).  

You need to know some things first:

• 1 mile = 1,760 yards 
• 1 yard = 3 feet 
• 1 foot = 30.48cm (you could approximate this to 30 if you like).
• 1 hour = 60 minutes 
• 1 minute = 60 seconds
• 1 hour = 3,600 seconds

I suggest the first thing we do is work out Usain Bolt's average speed over 100m.  His world record is 9.58 seconds over 100m.  

His average speed therefore is 100 ÷ 9.58 = 10.44 m/s

For children, the important thing is for them to appreciate what this figure tells us - it is saying that every second, Usain Bolt travels 10.44 metres.  (I'm ignoring the fact that his speed will change over the 100m because he is starting from a stationary position - we're just using his average speed here). 

The next thing we can do is work this out in metres per hour.  There are 3,600 seconds in an hour, so he would obviously be able to travel a lot further in one hour, if he could maintain this speed.  This is using a logical train of thought that the number we are looking for will be a lot bigger than his speed in m/s.  It's useful for children to have this idea of whether the answer they are looking for should be bigger or smaller than their previous answer, because this is a way of them self-regulating and checking if they are on the right track or not.

His speed in m/hour = 10.44 x 3,600 = 37,584

What we need to do next is convert our metres into miles.  The number of miles he'll cover will be a lot less than the number of metres, because a mile is a much bigger distance.  (We are therefore going to have to divide our previous answer by something to arrive at a smaller number).  We need to know what one mile is in metres.

In feet, 1 mile = 1,760 x 3 = 5,280 (because 1 yard = 3 feet)

In centimetres, 1 mile = 5,280 x 30.48 = 160,934.4 (because 1 foot = 30.48cm)

In metres, 1 mile = 160,934.4 ÷ 100 = 1,609.3 (because 1 metre = 100 centimetres)

We previously worked out that Usain Bolt travels 37,584 metres in one hour (in theory at least!) and we now need to work out how many miles this is.  We need to divide it by how many metres are in one mile, which we've just done above.

37,584 ÷ 1,609.3 = 23.4 miles per hour

This is perhaps a surprisingly low number, considering that Usain Bolt is such a fast runner.  It is well below the 30 miles per hour speed limit for cars in built up areas, well below my sixth form student's estimation, and if you look at the data below, far below the average speeds of many common mammals.  

Cheetah	68.0–75.0 mph
Mexican free-tailed bat (in flight)	99 mph
Hyena	37 mph
Big brown bat	40 mph
Common dolphin	40 mph
Zebra	40 mph
Tiger	40 mph
Coyote	40 mph
Greyhound (Domestic dog)	43 mph
Thomson's gazelle	43 mph
Onager	43 mph
Domestic Horse	43.97 mph
African wild dog	44 mph
Kangaroo	44 mph
Jackrabbit	45 mph
Blackbuck	50 mph
Hare	50 mph
Wildebeest	50.0 mph
Lion	50.0 mph
Springbok	55 mph
Pronghorn	55.0 mph

He's still the fastest human on Earth though!

As a footnote it is worth reflecting on the fact that the table above uses 'm' for miles, the same symbol as 'm' for metres.  This is a possible source of confusion for children and should be pointed out to them.  It is also the case that the 'per' is represented as the letter 'p' whereas they will always simply use a '/' in every other case when they use units.  

Source for speed data: https://en.wikipedia.org/wiki/Fastest_animals#Mammals