Question : Shreya hikes up a hill at 5 mph and comes down at 7 mph. If the total time taken for the two-way journey is 3 hours, what is the distance between the hilltop and the foothill?
Option 1: 8.75 miles
Option 2: 8 miles
Option 3: 9 miles
Option 4: 6.75 miles
Correct Answer: 8.75 miles
Solution :
Uphill speed = 5 mph
Downhill speed = 7 mph
Total time taken = 3 hr
Let $d$ be the distance, $t$ be the time taken to go uphill and $3-t$ be the time taken to go downhill.
⇒ $d = 5t$
⇒ $t = \frac{d}{5}$ ---------(i)
Also, $d= 7(3-t)$
⇒ $d = 21-7t$
⇒ $d = 21 -7(\frac{d}{5})$
⇒ $\frac{12d}{5} = 21$
⇒ $d = \frac{105}{12} = 8.75$
Hence, the correct answer is 8.75 miles.
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