Bluelagoon wrote:
Three bodies A, B and C start moving around a circular track of length 60m from the same point simultaneously in the same direction at speeds of 3 m/s, 5 m/s and 9 m/s respectively. When will they meet for the first time after they started moving?
A. 30 seconds
B. 60 seconds
C. 15 seconds
D. 10 seconds
E. 25 seconds
Let’s analyze the answer choices from the smallest to the largest.
D) 10 seconds
After 10 seconds, A, B, and C have moved 30 m, 50 m, and 90 m, respectively. While A and B haven’t completed one lap, C has completed one lap and 30 m more. We see that A and C meet at the same place on the track, but B doesn’t meet them at that place .
C) 15 seconds
After 15 seconds, A, B, and C have moved 45 m, 75 m, and 135 m, respectively. While A hasn’t completed one lap, B has completed one lap and 15 m more, and C has completed two laps and 15 m more. We see that B and C meet at the same place on the track, but A doesn’t meet them at that place.
E) 25 seconds
After 25 seconds, A, B and C have moved 75 m, 125 m, and 225 m, respectively. We see that A has completed one lap and 15 m more, B has completed two laps and 5 m more, and C has completed three laps and 45 m more. We see that each person is at a different place on the track.
A) 30 seconds
After 30 seconds, A, B, and C have moved 90 m, 150 m, and 270 m, respectively. We see that A has completed one lap and 30 m more, B has completed two laps and 30 m more and C has completed four laps and 30 m more. We see that all of them are at the same place on the track.
Alternate Solution:
Suppose that they meet after t seconds for the first time. In t seconds, they have covered a distance of 3t, 5t and 9t meters, respectively. Notice that the distance between A and B is 5t - 3t = 2t, A and C is 9t - 3t = 6t and B and C is 9t - 5t = 4t. If they are at the same spot after t seconds, all of 2t, 6t and 4t must be multiples of 60; say 2t = 60k, 6t = 60s and 4t = 60p. Then, t = 30k = 10s = 15p. Since t is a multiple of 30, 10 and 15; the smallest value of t is given by the LCM of these numbers. Therefore, the smallest value of t is LCM(30, 10, 15) = 30.
Answer: A