Multiple choice

A car travels $\dfrac{1}{3}^{rd}$ distance on a straight road with a velocity of 10 km/hr, next $\dfrac{1}{3}^{rd}$ with velocity 20 km/hr and the last $\dfrac{1}{3}^{rd}$ with velocity 60 km/hr. What is the average speed of the car in the whole journey?

  1. 4 km/hr

  2. 6 km/hr

  3. 12 km/hr

  4. 18 km/hr
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D Correct answer
Explanation

Average speed = Total Distance / Total Time. Let total distance be 3D. Time = D/10 + D/20 + D/60 = (6D+3D+D)/60 = 10D/60 = D/6. Average speed = 3D / (D/6) = 18 km/hr.

AI explanation

Using the harmonic mean formula for average speed when equal distances are travelled at different speeds, the average speed equals 3 divided by the sum of the reciprocals of the individual speeds. For the speeds of 10 km/hr, 20 km/hr, and 60 km/hr, this gives 3 divided by the quantity (1/10 plus 1/20 plus 1/60). Finding a common denominator of 60, the sum in the denominator becomes 6/60 plus 3/60 plus 1/60, which equals 10/60 or 1/6. The average speed is therefore 3 divided by 1/6, resulting in 18 km/hr.

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