Question

A motorboat covers a certain distance downstream in a river in 4 hours. It covers the same distance upstream in 5 hours. The speed of the motorboat in still water is 27 km/h.

What is the speed of the stream?

Answer 1

let the speed of the bot be v and the speed of the stream be u

then the relative speed wrt ground while going downstream becomes = v+u and while going upstream becomes v -u

now distance travelled = speed * time

let x be the distance travelled

therefore for downstream

x = ( 27 + u) *4 .............................................(a)

for upstream

x = ( 27 - u ) * 5 ..............................................(b)

therefore from a and b we get

( 27 + u) *4 = ( 27 - u ) * 5

9 u = 27

u = 3 km/h