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On a circular track, a motorcycle starts from point X and a truck starts from point Y, which is 500 m ahead of X in the direction of motion. The speed of the motorcycle is 20 m/s and that of the truck is 8 m/s. If the length of the track is 2.2 km, how much distance will the motorcycle have travelled when it overtakes the truck for the first time?

1. 845.5 m
2. 1,800 m
3. 800 m
4. 833.33 m

Correct answer: 833.33 m

Solution

The truck is 500 m ahead, so the initial gap is 500 m. Since the motorcycle is faster by 20−8 = 12 m/s, it must gain 2200−500 = 1700 m relative to the truck to overtake it for the first time on the circular track. Time taken = 1700/12 = 141.67 s, so motorcycle distance = 20 × 141.67 ≈ 833.33 m.

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