The average speed of a car running at the rate of 15 km/hour during the first 30 km and at 20 km/hour during the second 30 km and at 25 km/hour during the third 30 km, will be

Question

The average speed of a car running at the rate of 15 km/hour during the first 30 km and at 20 km/hour during the second 30 km and at 25 km/hour during the third 30 km, will be (A) 19.15 km/hour (B) 20 km/hour (C) 19.65 km/hour (D) 19.75 km/hour.

Tardigrade Admin · Accepted Answer

Here, the required average speed is equal to the harmonic mean of the three speeds = (3/(1)15 + (1)20+ (1/25) km/hour = (3×300/20+15+12) = (900/47) km/hour = 19.15 km/hour.

Q. The average speed of a car running at the rate of 15 km/hour during the first 30 km and at 20 km/hour during the second 30 km and at 25 km/hour during the third 30 km, will be

19.15 km/hour

20 km/hour

19.65 km/hour

19.75 km/hour.

Here, the required average speed is equal to the harmonic mean of the three speeds
$= \frac{3}{\frac{1}{15} + \frac{1}{20} + \frac{1}{25}}$ km/hour
$= \frac{3 \times 300}{20 + 15 + 12} = \frac{900}{47}$ km/hour = 19.15 km/hour.

Q. The average speed of a car running at the rate of 15 km/hour during the first 30 km and at 20 km/hour during the second 30 km and at 25 km/hour during the third 30 km, will be

19.15 km/hour

20 km/hour

19.65 km/hour

19.75 km/hour.

Here, the required average speed is equal to the harmonic mean of the three speeds =151​+201​+251​3​ km/hour =20+15+123×300​=47900​ km/hour = 19.15 km/hour.

Here, the required average speed is equal to the harmonic mean of the three speeds
$= \frac{3}{\frac{1}{15} + \frac{1}{20} + \frac{1}{25}}$ km/hour
$= \frac{3 \times 300}{20 + 15 + 12} = \frac{900}{47}$ km/hour = 19.15 km/hour.