Question : Dinesh makes four trips of equal distances. His speed on the first trip was 140 km/hr and in each subsequent trip, his speed was half of the previous trip. What is the average speed of Dinesh in these four trips?
Option 1: $40$ km/hr
Option 2: $44$ km/hr
Option 3: $\frac{112}{3}$ km/hr
Option 4: $\frac{124}{3}$ km/hr
Correct Answer: $\frac{112}{3}$ km/hr
Solution :
Let the distance be $x$ km.
Dinesh's speed on the first trip was 140 km/hr.
Time taken = $\frac{x}{140}$
His speed in 2nd trip = $\frac{140}{2}=70$ km/hr
Time taken = $\frac{x}{70}$
His speed in 3rd trip = $\frac{70}{2}=35$ km/hr
Time taken = $\frac{x}{35}$
His speed in 4th trip = $\frac{35}{2}$ km/hr
Time taken = $\frac{2x}{35}$
Total time taken = $\frac{x}{140}+\frac{x}{70}+\frac{x}{35}+\frac{2x}{35}=\frac{x+2x+4x+8x}{140}=\frac{15x}{140}=\frac{3x}{28}$
$\text{Average speed}=\frac{\text{Total distance}}{{\text{Total time}}}=\frac{4x}{\frac{3x}{28}}=4x×\frac{28}{3x}=\frac{112}{3}$ km/hr
Hence, the correct answer is $\frac{112}{3}$ km/hr.
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