Question

A man covers a distance with speed v1 and v2 in equal time period. Find the average speed.

Answer 1

initial speed=v1

let time be t1

therefore,distance=v1×t1

final speed=v2

let Time be t2

therefore,distance=v2×t2

average speed=(v1t1+v2t2)/(t1+t2)

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Answer 2

The average speed of the man is ( v1 + v2 ) / 2.

Given: A man covers a distance with speeds v1 and v2 in an equal period.

To Find: The average speed of the man.

Solution:

The average speed of a body can be founded by applying the formula which states that,

        Average speed = Total distance covered / Total time         ....(1)

Coming to the numerical, we are given;

The speed of the man in the first half of the journey = v1

The speed of the man in the second half of the journey = v2

Since the time required in both halves of the journey is equal, so we can say that the total time required is = t + t = 2t

So, the distance covered in the first half of the journey = v1 × t

the distance covered in the second half of the journey = v2 × t

Now, we can find the average speed by putting respective values in (1),

        Average speed = Total distance covered / Total time

                                   = (( v1 × t ) + ( v2 × t )) / 2t

                                   = t × ( v1 + v2 ) / 2t

                                   =  ( v1 + v2 ) / 2

Hence, the average speed of the man is ( v1 + v2 ) / 2.

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