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
OG-17 (DIAGNOSTIC TEST)
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As with all VIACs (Variables In the Answer Choices questions), we can solve this via the INPUT-OUTPUT approach or via an ALGEBRAIC approach.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
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
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Let the distance = 10 miles.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)
Let x = 5 miles per hour and y = 2 miles per hour.
Time for Aaron to jog 10 miles at a rate of 5 miles per hour = d/r = 10/5 = 2 hours.
Time for Aaron to walk 10 miles at a rate of 2 miles per hour = d/r = 10/2 = 5 hours.
t = total time spent jogging and walking = 2+5 = 7 hours.
The question stem ask for the distance that Aaron jogs (10 miles).
This is our target.
Now plug x=5, y=2 and t=7 into the answer choices to see which yields our target of 7.
Only C works:
(xyt)/(x+y) = (5*2*7)/(5+2) = 10.
The correct answer is C.
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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,
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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
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We can infer that the time t is defined as the total time spent jogging and walking. It's as if he knows exactly how long he wants to spend, and knows exactly the speeds at which he'll jog and walk. And based on that, he wants to determine how far he can go.Mo2men wrote:Dear Experts,
What does the stem ask for? I understood it as if I will use the total time to find NEW distance form home? How can In interpret t correctly?
Thanks
So there's no such thing as "new" or "old" distance. Imagine that before he leaves the house, he has a plan: "I want to go a total of t hours, and my speeds are x for jogging and y for walking. So that means I can jog a distance of d miles, then turn around and walk back the same d miles."
Did that help?
I posted a full algebraic solution here: https://www.beatthegmat.com/og-13-24-t288366.html#765096
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Harvard Graduate School of Education
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We can let d = the distance traveled when walking and jogging.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
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
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