The speed of a boat is 12 km/h in still water. It goes 18 km downstream and comes back in a total time of $6\frac{6}{7}$ hours. Find the speed of the stream (in km/h)

9

Speed of boat = 20 km/h

Speed of stream = S km/h

Downstream speed = ( 12 + S) km/h

Upstream speed = (12 - S) km/h

According to question ,

\(\frac{18}{12-S}\)  +  \(\frac{18}{12 + S}\) = \(\frac{48}{7}\) hours

\(\frac{18 × 12 + 18× 12 }{(12-S)(12+S)}\) = \(\frac{48}{7}\)

432 × 7 = 48 × ( 144 - S2 )

on solving , 

S2 = 81 

S = 9 km/h

SO , Speed of stream is 9 km/h