Problem Solving

Aaron will jog from home at x miles per hour and then walk back at y miles an hour on the same route. 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

jogging x mph for t1 h gives distance = x*t1
walking y mph for t2 h gives distance = y*t2
both the above distance are same, so x*t1=y*t2
Total time t= t1+t2
Putting the value of t1=t-t2 gives x*(t-t2)=y*t2, or x*t = (x+y)*t2
or, t2=x*t/(x+y)

Therefore. the required distance is y*t2 = xyt/(x+y) - choice C

I substituted numbers for x, y and t that would help pinpoint the correct answer choice. The numbers I chose were:

X = 10 (Jogged 10 miles per hour)
Y = 5 (Walked back at 5 miles per hour)
T = 3 (Total time spent jogging and walking. 1 jogging/2 walking back)

The distance Aaron jogged from his house is 10 miles so when we substitute the numbers in the answer choices we want to get to 10.

Going through all the answer choice, C is the only one that works:

(xyt)/x+y
=(10*5*3)/10+5
=150/15
=10