Problem Solving

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

very sensuous question

time jogged and time walked are 1/x and 1/y
combined time is t=1/x+1/y, t=(x+y)/xy, txy=x+y and distance is 1 (whole)=txy/(x+y)

[spoiler]why sensuous? Because ... [/spoiler]it could be also (x+y)/txy which ever GMAT likes in A-E

arpitad wrote:Aaron will jog from home at x miles per hour and then walk back home by the same route at y mph. 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 could also substitute numbers..

Say x=y=1mph.. therefore t=2hrs

now we spend 1 hr jogging.. sub x=y=1 and t=2..

Only C gives us 1hr.

t=d*(x+y)/xy

d=xyt/x+y

arpitad wrote:Aaron will jog from home at x miles per hour and then walk back home by the same route at y mph. 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 the distance to be traveled one way be "a", then
a/x + a/y = t (since a/x = time jogging, a/y = time walking)

Hence a = txy/(x+y)

Hence C

You could also pick numbers to help solve the problem in a different way than it was asked. if you set Distance = 20 and x = 5 and y = 2 you find that he jogs for 4 hours, walks for 10 hours for a total time spend of 14 hours.

So t = 14, x=5 and y = 2

Plug those numbers into the answer choices and only C xyt/x+y will give you the 20 as your distance from home.