Alphonsaj wrote:"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
Since A and B meet for the first time when A has traveled 4.5 laps at a rate of 70 seconds per lap, the time required for A and B to meet = (4.5)(70) = 315 seconds.
We can PLUG IN THE ANSWERS, which represent B's time per lap.
Since A is faster than B, B's time per lap must be GREATER than A's time per lap.
Eliminate B and D.
When the correct answer choice is plugged in, B will be exactly halfway around the track after traveling for 315 seconds.
E: 77 seconds
At a rate of 77 seconds per lap, the number of laps traveled by B in 315 seconds = 315/77 = 45/11 laps.
Since B is not exactly halfway around the track, eliminate E.
A: 90 seconds
At a rate of 90 seconds per lap, the number of laps traveled by B in 315 seconds = 315/90 = 35/10 = 3.5 laps.
Success!
The correct answer is
A.
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