Smriti Shashikumar wrote:Cathy and Tom are 20 miles apart and walk towards each other along the same route. Cathy walks at a constant rate that is 1 mile per hour faster than that of Tom's constant rate of 5 miles per hour. If Tom starts his journey 24 minutes after Cathy, how far from his original destination has Tom walked when the two meet?
A. 7 miles
B. 8 miles
C. 9 miles
D. 10 miles
E. 12 miles
Thanks for the help as always!
Before Tom starts to walk, Cathy travels alone at rate of 6 miles per hour for 2/5 of an hour:
Distance = r*t = 6*(2/5) = 12/5 miles.
Remaining distance = 20 - 12/5 = 88/5 miles.
When people travel toward each other, they WORK TOGETHER to cover the distance between them, so we ADD THEIR RATES.
Combined rate for Cathy and Tom = 6+5 = 11 miles per hour.
Since Tom's rate is 5 miles per hour, Tom will travel 5 of every 11 miles traveled by Cathy and Tom together.
Thus, Tom will travel 5/11 of the remaining distance:
(5/11)(88/5) = 8 miles.
The correct answer is
B.
Last edited by GMATGuruNY on Mon Feb 18, 2013 9:48 am, edited 1 time in total.
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