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Answer on Mechanics | Relativity Question for anjali sharma

Question #4583
A, B and C participated in a race around a circular track. A and B run in the same direction while C runs in the opposite direction. If the speeds of A, B and C are 10 m/s, 20 m/s and 30 m/s respectively, and the length of the track is 1000m, then after how long will they take to meet for the first time
125 seconds
100 seconds
200 seconds
150 seconds
Expert's answer
Let T be the time they'll meet for the first time. So, the distance A,B and C will run before meeting is 10T, 20T and 30T, respectively. The only place they can meet at is the start point. So, T must satisfy these conditions:
1000a = 10T, 1000b = 20T, 1000c = 30T,
where a,b,c are the number of laps A, B and C have to take before they met. We see that the minimum time to satisfy this condition is 100 seconds. By this time, A, B and C will take 1, 2 and 3 laps respectively.

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