Question

A motor boat whose speed is 18 km/hr in still water takes 1hr more to go 24 km upstream then to return downstream to the same spot . find the speed of the stream.

Answer 1

Sol:
Let the speed of the stream be x km/hr
Speed of the boat in still water = 18 km/hr
Speed of the boat in upstream = (18 - x) km/hr
Speed of the boat in downstram = (18 + x) km/hr

Distance between the places is 24 km.

Time to travel in upstream = d / (18 - x) hr
Time to travel in downstream = d / (18 + x) hr
Difference between timings = 1 hr

[24 / (18 - x)] - [24 / (18 + x)] = 1

⇒ 24 [1 / (18 - x)] - [1 / (18 + x)] = 1

⇒ [1 / (18 - x)] - [1 / (18 + x)] = 1/24

⇒ (18 + x - 18 + x) / (324 - x2) = 1/24

⇒ (2x) / (324 - x2) = 1/24

⇒ 324 - x2 = 48x

⇒ x2 - 48x + 324 = 0

⇒ (x + 54)(x - 6) = 0

x = - 54 or 6

Speed of the stream can not be negative.

Therefore, speed of the stream is 6 km/hr.

Answer 2

hello bro the answer is 6 km/ hr
this may help u