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Suresh went to Mathura which is 190 km far by certain modes of communication. He covers 77 km by bus, some distance by train and remaining by auto. Average speed of bus is 38.5 km / h, while that of train is 65 km / h and of the auto is 45 km / h. He covered total distance in 4 h. Find the distance covered by him in the auto?

Suresh went to Mathura which is 190 km far by certain modes of communication. He covers 77 km by bus, some distance by train and remaining by auto. Average speed of bus is 38.5 km / h, while that of train is 65 km / h and of the auto is 45 km / h. He covered total distance in 4 h. Find the distance covered by him in the auto? Correct Answer 38.25 km

Given:

The Total distance traveled to reach Mathura is 190 km.

The Distance covered by the bus is 77 km.

The Average speed of the bus is 38.5 km / h.

The Average speed of train is 65 km / h.

Average speed of auto is 45 km / h.

The Total time of journey = 4h

Formula used:

Basic unitary method.

The Distance = Speed × Time.

Calculation:

Let ‘T1 ‘h time required by traveling through train while ‘T2 ‘h time required by traveling through auto.

Time is taken to cover 77 km by bus = 77 / 38.5

= 2 h

So, the remaining journey has to be covered = Total time of journey - Time taken through the bus

= 4 - 2

= 2h

The Remaining distance to be covered by the train and auto = total distance - distance traveled by the bus

= 113 km

Now, the remaining distance has to covered by train and auto in the remaining time

 T1 + T2 = 2  ---(i)

65 × T1 + 45 × T2 = 113   ---(iv)

On solving equation 1 and 2, we get

T1 = 23 / 20 h

and T2 = 17 / 20 h

Distance covered by auto = speed of auto × T2

= 45 × 17 / 20

= 38.25 km

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