## Tuesday, October 10, 2006

### Cars and Mathematics

My sister married the most academically gifted man I have ever met. They studied together at university and enjoyed a wide and varied social life.

One day my brother in law arrived, with my sister beside him, in a very large motor car. The engine, I think, was urged from a very large lorry. The car was white with a pointed nose that protruded a good three feet in front of the fan belt. The rear of the car had no boot that I can recall but there was a ledge where suitcases or boxes could be strapped.

There were only two seats – and the driver and his passenger were probably about four and half feet off the ground. It was in fact the driving position of a very early Chelsea tractor. Naturally the car was topless. In those days it would have called an open tourer.

It was a remarkably noisy vehicle, as befitted its description as a `sports car’. I am not sure how long it took to reach 60 miles per hour. The engine did not purr – it chugged and gurgled majestically. There was no gentle emission, or puff of blue smoke – there was, quite simply, a continuous plume of carbon emissions.

Naturally there was a discussion of how many miles to the gallon the car did. In those days we did not have concern ourselves with litres. We could talk about gallons, quarts and pints. I think the car did eight miles to the gallon. If the car was driven fast (over 30 miles per hour) the consumption dropped to nearer to four miles to the gallon.

By now you should be able to work out the 11+ question. (Conversion of units is still a part of some 11+ examinations.)

Hint 1: We will need to change 4 miles to kilometres and then change 1 gallon to litres.

Hint 2: We know that 4 miles is about 6.4 kilometres.

Hint 3: We know too that 1 gallon is about 4.5 litres.

How many kilometres to the litre did the car do when it was driven quickly?