Question

a boat can travel 30km upstream and 28km downstream in 7hrs.if can travel 21km upstream and return in 5hrs.find the speed of a boat in still water and the speed of a stream.

Answer 1

We know that Speed = Distance / Time. This means Time = Distance / Speed
Let "u" be speed upstream and "d" be speed downstream
Using this we get:30/u + 23/d = 7 ------------- (i)
We are also given that the boat can travel up and down in 5 hours. This means:21/u + 21/d = 5 ------------- (ii)
Multiplying (ii) by 30/21, we get30/u + 30/d = 50/7 --------- (iii)
Subtracting (iii) from (i), we get: d = 49 km/hr
Inputting this in equation (i), we get u = 4.59km/hr
We know that Speed Upstream = Speed of boat - Speed of streamand Speed Downstream = Speed of boat - Speed of stream
From here we get two more equations:u = Sb - Sr, this means: 4.59 = Sb - Sr ----------- (iv)andd = Sb+Sr, this means: 49 = Sb + Sr ------------- (v)
Adding (iv) and (v), we get:Sb = 26.795 km/hr; substituting this value in equation (iv) we getSr = 22.205 km/hr
Please note, Sb = Speed of boat in still water and Sr = speed of stream.