Question

ROSA CAN JOG 5 MI DOWNHILL IN THE SAME TIME IT TAKES HER 3 MI TO JOG UPHIL. SHE JOGS 4MI FASTER DOWNHILL THAN UPHILL. WHAT IS HER JOGGING RATE EACH WAY

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Solution:
let the uphill speed = x
downhill speed will be = x+4
time = distance/speed
time to jog 3 MI uphill = 3/x
time to jog 5 MI uphill = 5/(x+4)
as per given, both time are same.
so,
\frac{3}{x}=\frac{5}{\left(x+4\right)}\xrightarrow{}3\left(x+4\right)=5x\xrightarrow{}3x+12=5x 12=5x-3x\xrightarrow{}12=2x\xrightarrow{}2x=12
x=\frac{12}{2}\xrightarrow{}x=6
hence,
uphill jogging rate = 6 mi/unit of time
downhill jogging rate = 6+4 = 10 mi/unit of time

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