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)
Let the distance = 10 miles.
Let x = 5 miles per hour and y = 2 miles per hour.
Time for Aaron to jog 10 miles at a rate of 5 miles per hour = d/r = 10/5 = 2 hours.
Time for Aaron to walk 10 miles at a rate of 2 miles per hour = d/r = 10/2 = 5 hours.
t = total time spent jogging and walking = 2+5 = 7 hours.
The question stem ask for the distance that Aaron jogs (10 miles).
This is our target.
Now plug x=5, y=2 and t=7 into the answer choices to see which yields our target of 7.
Only
C works:
(xyt)/(x+y) = (5*2*7)/(5+2) = 10.
The correct answer is
C.
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