A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is

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Q: 44 (IAS/2003)
A car travels the first one-third of a certain distance with a speed of 10 km/hr, the next one-third distance with a speed of 20 km/hr and the last one-third distance with a speed of 60 km/hr. The average speed of the car for the whole journey is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,8,11,8,5,5,1

keywords: 

{'average speed': [0, 2, 4, 2], 'speed': [0, 1, 2, 0], 'third distance': [0, 0, 1, 0], 'car': [0, 2, 12, 17], 'certain distance': [0, 0, 1, 1], 'km': [0, 0, 2, 1], 'whole journey': [0, 0, 1, 1]}

To find the average speed of the car for the whole journey, we can use the concept of harmonic mean.

Let`s assume that the total distance is `d`. Since the car travels one-third of the distance at each speed, each one-third distance would be (d/3).

The time taken to cover the first one-third distance at 10 km/hr is (d/3) / 10 = d/30 hours.

The time taken to cover the next one-third distance at 20 km/hr is also (d/3) / 20 = d/60 hours.

The time taken to cover the last one-third distance at 60 km/hr is (d/3) / 60 = d/180 hours.

The total time taken for the entire journey is (d/30) + (d/60) + (d/180) = (6d + 3d + d)/180 = 10d/180 = d/18 hours.

Now, the average speed is calculated by dividing the total distance (d) by the total time taken (d/18):

Average speed = d / (d/18) = 18 km/hr.

Therefore, the average speed of the car for the whole journey is 18 km/hr.