Question : Kabir climbs up a hill at a speed of 3 miles per hour and comes down at 5 miles per hour. If the total time taken for the total journey is 10 hours, then what was the distance between the hilltop and the foothills?
Option 1: 3.75 miles
Option 2: 18.75 miles
Option 3: 37.5 miles
Option 4: 20.5 miles
Correct Answer: 18.75 miles
Solution :
Uphill speed, $s_1$ = 3 miles per hour
Downhill speed, $s_2$ = 5 miles per hour
Average speed = $\frac{2s_1s_2}{s_1+s_2}$ = $\frac{2×3×5}{3+5}$ = $\frac{30}{8}$
Total time = 10 hours
Total distance = Average speed × total time $=\frac{300}{8}=\frac{75}{4}= 37.5$ miles
$\therefore$ Distance between the hilltop and the foothills $=\frac{37.5}{2}= 18.75$ miles
Hence, the correct answer is 18.75 miles.
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