Carcass 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. \(7.5\pi\)
E. \(45\pi\)
To get a better idea of what's happening, let's sketch the set-up:
Mary is faster than Kate, we can say that Kate has a 250 meter head start. In other words, when Mary closes that 250-meter gap, she will pass Kate for the FIRST time.
However, since we want to find the time for Mary to pass Kate for the SECOND time, we can say that Kate has a 750 meter head start.
So we want to determine the time it takes Mary to close the gap from 750 meters to 0 meters.
Mary runs 1000 meters every five minutes and Kate runs 1000 meters every six minutes. Speed = distance/timeMary's speed = 1000 meters/5 minutes = 200 meters per minuteKate's speed = 1000 meters/6 minutes ≈ 167 meters per minute200 meters per minute -
167 meters per minute =
33 meters per minuteSo, the distance gap between Mary and Kate CLOSES at a rate of
33 meters per minuteWe want to reduce the gap by 750 meters
Time = distance/rateSo, time = 750/
33STOP!! Before we perform this somewhat tedious calculation, we should scan the answer choices.
When we do so, we see that the answer choices are quite spread apart, which means we can be quite aggressive with our estimation.
So, rather than divide by 33, let's divide by 30
That is, 750/
33 ≈ 750/
30 = 25
So, the correct answer is close to 25
Answer: B
Cheers,
Brent
_________________
Brent Hanneson - founder of Greenlight Test Prep