A car moves from `X` to `Y` with a uniform speed `v_u` and returns to `Y` with a uniform speed `v_d`. The average speed for this round trip is :

Options

A. `sqrt(v_(u)v_(d))`
B. `(2v_(d)v_(u))/(v_(d)+v_(u))`
C. `(v_(u)+v_(d))/(2)`
D. `(v_(d)v_(u))/(v_(d)+v_(u))`

Answer

b

Explanation

Let x be the distance between X and Y.
Average speed `=("total distance")/("total time")`
`rArr u_(av)=(x+)/((x)/(v_(u)+(x)/(v_(d)))`
`rArr v_(av)=(2v_(d)v_(u))/(v_(d)+v_(u))`