Ratio and proportion

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

Have you ever wondered what it would be like to race against Usain Bolt?

Is there a temperature at which Celsius and Fahrenheit readings are the same?

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400 metres from B. How long is the lake?

Can you decide whose drink has the strongest blackcurrant flavour from these pictures?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.