A and B run the same way round a circular track from the same point, with speeds in the ratio 5 : 3. At how many different points of the track do they meet?

Explanation

1. 01

   With speeds $5k$ and $3k$ on a track of length $L$, they meet every $\frac{L}{2k}$, when A has run $\frac{5L}{2}$: 2.5 laps.

2. 02

   So the meetings fall at half a lap and at the start, alternately: 2 points, which is $5 - 3$.