In a race of L metres, 'A beats B by x m' means B has run L − x m when A finishes. 'A gives B a start of x m' means B starts x m ahead.
1Comparing runners
If A beats B by x m in L m, their speeds are in the ratio L : (L − x)
A beats B by x m and B beats C by y m in an L m race ⇒ A beats C by L − (L − x)(L − y)/L metres
Dead heat: both reach the finishing post at the same time