abhimahna wrote:
VeritasPrepKarishma wrote:
Responding to a pm:
"A" and "B" run around a circular track starting from the same point simultaneously in the same direction. "A" meets "B" for the first time when "A" is exactly in the middle of his 5th round. If "A" is faster than "B" and take 70 seconds to complete 1 lap, how long will B take to complete 1 lap?
A) 90 seconds
B) 54.44 seconds
C) 110 seconds
D) 63 seconds
E) 77 seconds
A is faster than B. Every second he increases distance between A and B. They will meet for the first time again when he increases distance between them by one full circle. (Say the lap is of 100m. He keeps increasing distance between them. When he is 90 m ahead of him, it is the same as 10 m behind him because they are moving in a circle. Finally when he is 100 m ahead of him, he is exactly 1 lap ahead and hence both are at the same point).
A takes 70 secs for one full lap. So he covers 4.5 laps in exactly 70*4.5 = 315 seconds.
In 315 secs, B completes 3.5 laps. So for each lap, he takes 315/3.5 = 90 secs
Answer (A)
How did you get "In 315 secs, B completes 3.5 laps."? Please elaborate.
DivyadishaA covers 4.5 laps in 315 seconds. This is when they meet. So B has also been running for 315 seconds. How much distance will he cover in this time?
Think about it: If B was still on his first lap, A would have met him in his second lap. Why? Because B would be somewhere on the circular path when A takes his second lap. So he would have met B then. But A met him for the first time after 4.5 laps.
Since they are both running in the same direction, till the time they cover equal number of laps (perhaps A is very slightly faster than B), they don't meet. B lags behind A. But when A covers a distance of 1 lap more than B, he has to cross B again (since they are running on the same circular path).
Try to draw a diagram to imagine it. They meet for the first time when A covers exactly 1 lap more than B.
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Karishma
Veritas Prep GMAT Instructor
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