### Jumping

from

nrich.maths.org/7407
Ben is hoping to enter the long jump at his school sports day.

One day I saw him manage quite a good jump.

However, after practising several days a week he finds that he can jump half as far again as he did before.

This last jump was $3.75$ metres long.

So how long was the first jump that I saw?

Now Mia has been practising for the high jump.

I saw that she managed a fairly good jump, but after training hard, she managed to jump half as high again as she did before.

This last jump was $1.20$ metres.

So how high was the first jump that I saw?

How did you work these out?

Can you find any other ways of finding a solution?

Which way do you prefer? Why?