EricKryk wrote:Aaron will jog from home at x miles per hour and then walk back home by the same route at y miles per hour. How many miles from home can Aaron jog so that he spends a total of t hours jogging and walking?
(A) xt/y
(B) (x+t)/(xy)
(C) (xyt)/(x+y)
(D) (x+y+t)/(xy)
(E) [(y+t)/x] - (t/y)
When the answers have variables, plug in your own numbers.
Let's say Aaron jogs at x = 5 miles/hour and walks at y = 2 miles/hour.
Now we need a distance.
In a rate problem, when the distance is undefined, plug in your own number for the distance.
Let's say the distance = 10 miles.
Time = Distance/Rate
If Aaron jogs at x= 5 miles/hour, it will take him 10/5 = 2 hours to jog the 10 miles.
If Aaron walks at y = 2 miles/hour, it will take him 10/2 = 5 hours to walk the 10 miles.
Since t is the total time spent jogging and walking, t = 2 + 5 = 7.
The question wants to know how far Aaron can jog. With our numbers, he's jogging 10 miles. Which answer choice = 10?
A. xt/y = 5(7)/2 = 17.5. Incorrect.
B. (x+t)/xy = (5+7)/(5*2) = 12/10. Incorrect.
C. (xyt)/(x+y) = (2*5*7)/(2+5) = 70/7 = 10. Success!
D. (x+y+t)/(x+y) = (2+5+7)/(2+5) = 14/7 = 2. Incorrect.
E. [(y+t)/x] - (t/y) = [(2+7)/5] - (7/2) = 9/5 - 7/2 = -17/10. Incorrect.
Since only answer choice C gave us the 10 miles we were looking for, the correct answer is
C.
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
