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Question

A circular field has a circumference of 360 km. Two cyclists Sumeet and Johan start together and can cycle at speeds of 12 km/hr and 15 km/hr, respectively, round the circular field. After how many hours will they meet again at the starting point?


Solution

Johan is the faster cyclist. When Johan crosses Sumeet he would have travelled the entire circular field more than Sumeet and will then be able to cross him and meet him again. 

Johan completes one more round than Sumeet and when they meet he is one more round ahead of him, which in turn means that he has travelled $$360$$ kms more than Sumeet when they meet.

Let the time at which they meet be equal to '$$t$$'.
$$ 15 \times t - 12 \times t = 360$$
$$ 3 \times t = 360 $$
Thus $$t = 120$$ hours.

Physics

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