A person travels half of a distance at an average velocity of 24 km.`h^(-1)`. At what average velocity should he move to cover the second half of the path so that his average velocity for the total path becomes 32 km . `h^(-1)`?

Explanation

Let the total length of the path = 2s km.
`:.` Time required to cover the first half of the path = `(s)/(24)`h.
If the man travels the total path with an average velocity of 32 km`.h^(-1)` , then the total time by him = `(2s)/(32) = (s)/(16)` h.
`:.` Time required to cover the second half of the path
`= (s)/(16)-(s)/(24) = (s)/(48) `h
`:.` Average velocity of second half
`= ("distance")/("time") = (s)/((s)/(48)) = 48 "km. h"^(-1)`