A person walking in a straight line, covers half of the distance to be travelled with a speed of `v_(0).` For half of the time, required to complete the remaining distance, he walks with a speed of `v_(1)` and for the remaining half time his speed is `v_(2)` What is the person's average speed during this complete walk ?

Options

A. `(v _(1) + v _(2))/( 2)`
B. `(2v _(1) + v _(2))/(v _(1) + v_(2))`
C. `(2v _(1) +v _(2))/(v _(1) + v _(2))`
D. `(L (v _(1) + v _(2)))/(v _(1) v _(2))`

Answer

C

Explanation

Time taken to travel firest half distance `t _(1) = ((1)/(2))/(v _(1)) = (l)/(2v _(1))`
Time taken to travel second half distance
`t _(2) = ((l)/(2) )/(v _(2)) (1)/(2v _(2))`
Total time `= t _(1) + t _(2) = (l)/(2v _(1)) + (l)/(2v _(2)) = (l)/(2) [ (1)/(v _(1)) + (1)/(v_(2))]`
We know that,
`V _(av)=` Average speed =` ("total distance")/("total time") = (l)/(t _(1) +t _(2))`
`= (l)/((l)/(2) [ (1)/( v _(1)) + (1)/(v _(2))]) = (2v _(1) v _(2))/(v _(1) + v _(2))`