chieftang wrote:Starting at the same time and from the same point on a circular track, Bill and Chris run laps in the same direction. Bill runs one lap every 1 1/3 minutes. Chris runs one lap every 2 1/2 minutes. After how many minutes will they both arrive simultaneously at the starting point?
(A) 6 minutes
(B) 10 minutes
(C) 16 minutes
(D) 20 minutes
(E) 22 minutes
Source: MOEMS problem bank.
ALWAYS LOOK AT THE ANSWER CHOICES.
Bill's rate = 4/3 minutes per lap.
Chris's rate = 5/2 minutes per lap.
In order for Bill and Chris both to arrive back at the starting point, the number of laps run by each runner must be an integer.
Thus, when the correct answer choice is divided by each rate, the result in each case must be an integer.
To divide by the fractions above, we multiply by their reciprocals: 3/4 and 2/5.
Thus, the correct answer choice must be a multiple of 4 and 5.
The correct answer is
D.
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