WholeLottaLove 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
From the onset I kind of figured you could solve with LCM's but I wasn't entirely sure why. I tried solving by figuring out how long it would take each of them to make one complete revolution and keep counting until their times aligned but I think that is incorrect because we're trying to figure out how long it takes for them to "meet up" we cannot solve that way. Is this correct?
If that is the case, then we need to figure out their relative speeds to determine when each body (let's call them A, B, C for the slow, medium and fast objects respectively) reaches the other.
B's relative rate to A is 5-3 = 2m/second so it takes B 30 seconds to move 60 meters away from A. In other words, at the 30 second mark, A and B are next to one another. A has traveled 90 meters and B has traveled 150 meters.
C's relative rate to A is 9-3 = 6m/second so it takes C 10 seconds to move 60 meters away from A. Every 10 seconds, it moves 60 meters (one full revolution) away from A. In 30 seconds (the time it takes A and B to meet up) it is 3 full revolutions ahead of A but is also next to it on the circle.
ANSWER A. 30 seconds.
A. 30 seconds
B. 60 seconds
C. 15 seconds
D. 10 seconds
E. 25 seconds
From the onset I kind of figured you could solve with LCM's but I wasn't entirely sure why. I tried solving by figuring out how long it would take each of them to make one complete revolution and keep counting until their times aligned but I think that is incorrect because we're trying to figure out how long it takes for them to "meet up" we cannot solve that way. Is this correct?
If that is the case, then we need to figure out their relative speeds to determine when each body (let's call them A, B, C for the slow, medium and fast objects respectively) reaches the other.
B's relative rate to A is 5-3 = 2m/second so it takes B 30 seconds to move 60 meters away from A. In other words, at the 30 second mark, A and B are next to one another. A has traveled 90 meters and B has traveled 150 meters.
C's relative rate to A is 9-3 = 6m/second so it takes C 10 seconds to move 60 meters away from A. Every 10 seconds, it moves 60 meters (one full revolution) away from A. In 30 seconds (the time it takes A and B to meet up) it is 3 full revolutions ahead of A but is also next to it on the circle.
ANSWER A. 30 seconds.
LCM of time works for a question of a different type:
When will they meet for the first time AT THE STARTING POINT after they started moving?
Time take by A to cover a circle = 60/3 = 20 sec
Time taken by B to cover a circle = 60/5 = 12 sec
Time taken by C to cover a circle = 60/9 sec
So every 20 sec, A will be at the starting point.
Every 12 secs B will be at the starting point.
Every 60/9 sec, C will be at the starting point.
Taking their LCM, we get 60. So every 60 sec, all three will be at the starting point. All meet for the first time at the starting point after they start moving after 60 sec.