Challenge Level

Boris: 5 steps 100 - finished

Spike: 4 steps $\times$20 80 - finished (21 + 80 $\gt$ 99)

Percival: 3 steps 60 - not finished (38 + 60 $\lt$ 99) Last place

$\times$19 95 (4 steps to go)

76 (21 + 76 = 97 $\Rightarrow$ 2 steps to go) winner

Boris: $99$ steps

Spike: $99 - 21 = 78$ steps

Percival: $99 - 38 =61$ steps

In each time unit, Boris runs $5$ steps, Spike runs $4$ steps, Percival runs $3$ steps.

Boris: $99$ steps, $99 \div 5 = 19\frac{4}{5}$

Spike: $78$ steps, $78 \div 4 = 19\frac{1}{2}$

Percival: $61$ steps, $61 \div 3 = 20\frac{1}{3}$

Therefore they finish in the order Spike, Boris, Percival.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.