BTGmoderatorDC wrote:Mary and Kate are running clockwise around a circular track with a circumference of 500 meters, each at her own constant speed. Mary runs 1000 meters every five minutes and Kate runs 1000 meters every six minutes. If Mary and Kate start opposite one another on the circular track, how many minutes must Mary run in order to pass Kate and catch her again?
A. 7.5
B. 22.5
C. 750
D. 7.5Ï€
E. 45Ï€
Since Mary is behind Kate by 250 meters -- half the circumference of the track -- she will catch up to Mary when she has traveled 250 meters more than Kate.
To catch up to Kate a second time, Mary must then travel one more lap than Kate -- in other words, 500 meters more than Kate.
Implication:
To catch up to Kate TWICE, Mary must travel a total of 750 meters more than Kate.
When people compete, SUBTRACT THEIR RATES.
Mary's rate = (1000 meters)/(5 minutes) = 200 meters per minute.
Kate's rate = (1000 meters)/(6 minutes) = 500/3 meters per minute.
Rate difference = 200 - 500/3 = 600/3 - 500/3 = 100/3 meters per minute.
Implication:
Every minute, Mary travels 100/3 meters more than Kate.
Since Mary must travel 750 meters more than Kate -- and every minute she travels 100/3 meters more than Kate -- the time for Mary to catch up to Kate twice = 750/(100/3) = (750*3)/100 = 7.5 * 3 = 22.5 minutes.
The correct answer is
B.
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