Question) Speed of boat ins still water is 15 km/h. It goes 30 km upstream and returns back ate the same point in 4 hours 30 minutes. Find the speed of the stream.

Please find this answer

Let speed of boat = 'x' km/h = 15 km/h and speed of stream = 'y' km/h

Speed upstream = (x+y) km/h
Speed downstream = (x-y) km/h

Speed = Distance
                Time

=> Time = Distance
                    Speed

Let time taken for upstream be t₁ = 30   hrs
                                                        ​ x-y

Let time taken for downstream be t₂ = 30   hrs
                                                             x+y

Total time taken = t₁ + t₂ = 30   +   30    =   4.5
                                            x+y      x-y  


=> 30   +   30   =   4.5
   15+y     15-y


=> 30(15-y) + 30(15+y)   =   4.5
               15² - y²


=> 30{ (15-y) + (15+y) }   =   4.5(225 - y²)

=> 30(15 - y + 15 + y)  =  4.5(225 - y²)

=> 30 x 30 = 4.5(225 - y²)

=> 900 x 10 = 45(225 - y²)

=> 225 - y² = 9000/45

=> 225 - y² = 200

=> y² = 25

=> y = ​± 5​ km/h

Speed cannot be in negative,

=> y = 5 km/h

∴ S​peed of stream = 5 km/h


Hope this helps!