a motorboat whose speed is 9km/hr in still water,goes 15km downstream and comes back in a total time of 3hrs45min.find the speed of the stream?

T = time for downstream, t = time for upstream travel.

T + t = 3 hrs 45 min = 15/4 hrs.

For downstream, distance/velocity = time,

15/(V + v) = T

15/(9 + v) = T       ... (1)

Similarly,

15/(9 -  v) = t    ... (2)     ...where V - Speed of boat, v - speed of stream.

Add (1) and (2)

15/(9 + v) + 15/(9 -  v) = T + t

15(18)/(81 - v²)  = 15/4

v² = 81 - (18x4) = 9

v = sped of stream is 3 km/hr.

Regards,

Team,

TopperLearning.