Question : A man takes 6 hours to go to a place and come back by walking both ways. He could have saved 2 hours by riding both ways. The distance covered in the whole journey is 20 miles. What is the average speed for the whole journey if he goes by walking and comes back by riding?
Option 1: 8 miles/hr
Option 2: 5 miles/hr
Option 3: 6 miles/hr
Option 4: 4 miles/hr
Correct Answer: 4 miles/hr
Solution :
We know,
Average speed = $\frac{\text{Total distance}}{\text{Total time}}$
Time has taken on walking both ways at constant speed = 6 hours
Time has taken on walking one way at constant speed = $\frac{6}{2}$ = 3 hours
He gained 2 hours by riding both ways.
Time taken on riding both ways at constant speed = 6 – 2 = 4 hours
Time has taken on riding one way = $\frac42$ = 2 hours
Total time taken if he goes walking and comes by riding = 3 + 2 = 5 hours
Total journey distance = 20 miles
$\therefore$ Average speed $= \frac{20}{(3 + 2)}=\frac{20}{5}$ = 4 miles per hour
Hence, the correct answer is 4 miles/hour.
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