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A robber fleeing a security guard had a 200 m head start. If the ratio of the security guard's speed to the robber's speed is 7 : 5, how far (in metres) does the robber travel before being caught? (Original: thief 150 m ahead, speed ratio police:thief = 5:4.)

1. 200
2. 600
3. 400
4. 350

Correct answer: 600

Solution

Let the thief's speed = 4k and policeman's speed = 5k. Relative speed (gain) = k. Time to close 150 m gap = 150/k. In this time, the thief travels 4k x (150/k) = 600 m.

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