Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Swimmers

Or search by topic

Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Here's a
sample of the good reasoning from Maithra of Henrietta Barnett
School, and others :

At their first crossing A has swum 30 and B has swum x - 30 , where x is the pool length.

At their second crossing A has now swum x + 20 in all and B has swum 2x - 20

There respective distances will keep in a fixed ratio because their speeds are in a fixed ratio.

This equation expresses that

and can be solved to find the
length of the pool.

x is zero or 70, and a pool of length zero is not our interest here so 70 m is the pool's length.

Here's another line of reasoning :

At first crossing A and B have swum one length between them, and A swam 30m of that length.

At second crossing A and B have swum two more lengths between them, so A will have swum 60m of those two lengths.

A has swum 90m in all, and that is one whole length plus a further 20m . So the pool is 70m long.