Joy Shaha wrote:Q. James started from his home and drove eastwards at a constant speed. Exactly 90 minutes after James stated from his home, his brother Patrick started from the same point and drove in the same direction as James did at a different constant speed. Patrick overtook James exactly 90 minutes after Patrick started his journey and then continued driving at the same speed for another 2 hours. By what percentage should Patrick reduce his speed so that James could catch up with Patrick in exactly 8 hours after Patrick overtook James?
A. 25%
B. 33%
C. 50%
D. 67%
E. 75%
Let J's rate = 12 miles per hour.
P catches up to J after J has traveled for 180 minutes (3 hours).
In 3 hours, the distance traveled by J = rt = (12)(3) = 36 miles.
Since P starts 3/2 hours after J, P must travel these 36 miles in only 3/2 hours.
Thus, P's rate = d/t = 36/(3/2) = 24 miles per hour.
Over the next 2 hours, the difference between P's distance and J's distance = (P's rate - J's rate)(time) = (24-12)(2) = 24 miles.
Implication:
After 2 hours, P is 24 miles ahead of J.
Since J must catch up to P after another 6 hours -- 8 hours after P overtook J -- the required catch-up rate = (catch-up distance)/(catch-up time) = 24/6 = 4 miles per hour.
Implication:
For J to catch up to P in another 6 hours, J must travel 4 miles per hour FASTER than P.
Since J's rate = 12 miles per hour, P's rate must decrease to 8 miles per hour, with the result that J's rate will be 4 miles per hour faster than P's rate.
P's percent decrease from 24 miles per hour to 8 miles per hour = (24-8)/24 * 100 = (16/24)(100) = (2/3)(100) ≈ 67%.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
