Problem Solving

j_shreyans wrote:Aron 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 Aron 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

OAC

As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach (as Mitch has done) or via an ALGEBRAIC approach.
Typically, when the answer choices look complex (as they do here), I find the INPUT-OUTPUT approach easier.
However, the algebraic approach isn't too bad.

Let's let d = the number of miles (distance) that Aaron jogs.
This means that d also = 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