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A car travels from city A to city B, $120 km$ apart at an average speed of $50 kmph$ . It then makes a return trip at an average speed of $60 kmph$ . It covers another $120 km$ distance at an average speed of $40 kmph$ . The average speed over the entire $360 km$ will be

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60kmph

30kmph

50.5kmph

48.64kmph

answer is D.

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Detailed Solution

It is given that, a car travels from city A to city B.
The two cities are 120km apart. Average speed of car is

50 km / hr

.
It then makes a return trip at an average speed of

60 km / hr .

It covers another 120km distance at an average speed of

40 km / hr

.
The speed of the object is the ratio of the distance traveled by the object over the time taken.
Thus, the time taken from city A to city B is,

t 1 = 12050 kmph

The time taken in return trip is,

t 2 = 12060 kmph

And, the time taken in covering another distance is,

t 3 = 12040 kmph

Total distance d is 360km.
Therefore, the average speed is,

S = d t 1 + t 2 + t 3 ⇒ S = 360 12050 + 12060 + 2040 ⇒ S = 360 7.4 ⇒ S = 48.64 kmph

Thus, the average speed is 48.64kmph.
Therefore, option (4) is correct.

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