Problem Solving

acegmat29 wrote: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

As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach or via an ALGEBRAIC approach.

Here's an algebraic approach:

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

Hi acegmat29,

This question can be solved by TESTing VALUES. I'm going to give you a couple of hints so that you can attempt this question on your own...

1) Since this question has so many variables, you want to make sure that the variables are easy to work with. Try using X = 3 miles/hour and Y = 2 miles/hour and set each distance at 6 miles.
2) You'll have to do some simple calculations to figure out the time traveled in each direction and the total time (T), which you'll need to answer the question.
3) TEST those values in the answer choices; you're looking for answer that equals 6.

GMAT assassins aren't born, they're made,
Rich

acegmat29 wrote: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

We can let d = the distance traveled when walking and jogging.

Thus, the jogging time is d/x and the walking time is d/y. Since the total time is t:

d/x + d/y = t

Multiply the entire equation by xy:

dy + dx = txy

d(y + x) = txy

d = txy/(y + x)

Answer: C