Discussion

In a 500 m race, P and Q have speeds in the ratio of 3 : 4. Q starts the race when P has already covered 140 m.

What is the distance between P and Q (in m) when P wins the race?

Answer: A

The gap is 20 m.

When Q starts, P still has 500 - 140 = 360 m to run. In the same time Q covers distance in the ratio 4 : 3:

\[ \text{Q's distance} = 360 \times \frac{4}{3} = 480\ \text{m} \]

So when P finishes at 500 m, Q is at 480 m, 20 m behind. P does win, since Q would need 500 m.

140 is only P's head start. A gap of 40 or 60 m would need a different speed ratio, since with 3 : 4 Q gains exactly 120 m on P over P's last 360 m.

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