mymbadreamz wrote:
I'm lost with this question too. Can someone please explain? thanks!
Aaron will jog home at x miles per hour and then walk back home on 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
Algebraic approach:Say the distance Aaron jogs is
d miles, notice that the distance Aaron walks back will also be
d miles (since he walks back home on the same route).
Next, total time
t would be equal to the time he spends on jogging plus the time he spends on walking:
\frac{d}{x}+\frac{d}{y}=t -->
d(\frac{1}{x}+\frac{1}{y})=t -->
d=\frac{xyt}{x+y}.
Answer: C.
Number picking approach:Say the distance in 10 miles,
x=10 mile/hour and
y=5 mile/hour (pick x and y so that they will be factors of 10).
So, Aaron spends on jogging 10/10=1 hour and on walking 10/5=2 hours, so total time
t=1+2=3 hours.
Now, we have that
x=10,
y=5 and
t=3. Plug these values into the answer choices to see which gives 10 miles. Only answer choice C fits:
\frac{xyt}{x+y}=\frac{10*5*3}{10+5}=10.
Answer: C.
Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.
Hope it helps.
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84% (02:54) correct
