Problem Solving

Vincen wrote: ↑

Wed Feb 23, 2022 3:59 am

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) \(\dfrac{xt}{y}\)

(B) \(\dfrac{x+t}{xy}\)

(C) \(\dfrac{xyt}{x+y}\)

(D) \(\dfrac{x+y+t}{xy}\)

(E) \(\dfrac{y+t}{x}-\dfrac{t}{y}\)

Answer: C

Source: Official Guide

Let d = the number of miles (distance) that Aaron JOGS.
This also means that d = the distance that Aaron WALKS.

Let's start with a WORD EQUATION:

total time = (time spent jogging) + (time spent walking)
In other words: t = (time spent jogging) + (time spent walking)
Since time = distance/speed, we can write: t = d/x + d/y [our goal is to solve this equation for d]
The least common multiple of x and y is xy, so we can eliminate the fractions by multiplying both sides by xy. When we do so, we get...
txy = dy + dx
Factor right side to get: txy = d(x + y)
Divide both sides by (x+y) to get: txy/(x+y) = d


So, the correct answer is C

Cheers,
Brent