A runner's average speed reduces by 25% every hour. If he runs 16 km i

A runner’s average speed reduces by 25% every hour. If he runs 16 km in the first hour and he runs for 3 hours, then what is his overall average speed?

12 km/hr

12.33 km/hr

10.33 km/hr

13 km/hr

Answer is Right!

Answer is Wrong!

This question was previously asked in

UPSC CAPF – 2022

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The runner runs for 3 hours. In the first hour, the speed is 16 km/hr, so the distance covered is $16 \times 1 = 16$ km. The speed reduces by 25% every hour. Speed in the second hour = $16 \times (1 – 0.25) = 16 \times 0.75 = 12$ km/hr. Distance covered in the second hour = $12 \times 1 = 12$ km. Speed in the third hour = $12 \times (1 – 0.25) = 12 \times 0.75 = 9$ km/hr. Distance covered in the third hour = $9 \times 1 = 9$ km. The total distance covered in 3 hours is $16 + 12 + 9 = 37$ km. The total time taken is 3 hours. The overall average speed is Total Distance / Total Time = $\frac{37}{3}$ km/hr. $\frac{37}{3} \approx 12.333$ km/hr.

Average speed is calculated as total distance divided by total time. The speed changes each hour, so we must calculate the distance covered in each hour and sum them up.

Note that average speed is not simply the average of the speeds in each hour (which would be $(16+12+9)/3 = 37/3 \approx 12.33$ km/hr in this specific case because each speed was maintained for one hour). The formula for average speed is always Total Distance / Total Time, which is the correct approach here.

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