Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### Advanced mathematics

### For younger learners

# Circuit Training

Why do runners always run around the track in an anticlockwise direction?

Do they develop a clinical lean?

Mike and Monisha meet at the race track, which is $400 \; \text{m}$ round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise, normally Mike can complete a circuit of the track in two thirds of the time Monisha takes.

They agree to stop when they both meet at the start again. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?

## You may also like

### There's a Limit

### Not Continued Fractions

Or search by topic

Age 14 to 16

Challenge Level

Why do runners always run around the track in an anticlockwise direction?

Do they develop a clinical lean?

Mike and Monisha meet at the race track, which is $400 \; \text{m}$ round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise, normally Mike can complete a circuit of the track in two thirds of the time Monisha takes.

They agree to stop when they both meet at the start again. Where will they meet on their way around and will they ever meet at the start again? If so, after how many circuits?

Explore the continued fraction: 2+3/(2+3/(2+3/2+...)) What do you notice when successive terms are taken? What happens to the terms if the fraction goes on indefinitely?

Which rational numbers cannot be written in the form x + 1/(y + 1/z) where x, y and z are integers?