## 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

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### 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

by Vincen » Wed Feb 23, 2022 3:59 am

00:00

A

B

C

D

E

## Global Stats

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) $$\dfrac{y+t}{x}-\dfrac{t}{y}$$

Source: Official Guide

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### Re: Aaron will jog from home at $$x$$ miles per hour and then walk back home by the same route at $$y$$ miles per hour.

by [email protected] » Thu Feb 24, 2022 7:56 am
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) $$\dfrac{y+t}{x}-\dfrac{t}{y}$$

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

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

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