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
