Question

A race boat covers a distance of 60km downstream in one and a half hours. It covers this distance upstream in 2 hours. The speed of the race boat in still water is 35km/hr. find the speed of the stream.
$
  (a){\text{ 5 km/hr}} \\
  (b){\text{ 5 m/s}} \\
  (c){\text{ 0}}{\text{.5 km/s}} \\
  (d){\text{ 6 km/m}} \\
 $

Answer 1

Hint – In this question let the speed of the boat in still water be x km/hr and speed of boat in stream be y km/hr. Derive relations between these variables by considering the concept of upstream and downstream. Solve the questions to get the answer.
Complete step-by-step answer:
Let the speed of the race-boat in still water be x km/hr.
And the speed of the stream be y km/hr.
So the downstream (D.S) speed = speed of race-boat + speed of stream.
And the upstream (U.S) speed = speed of race-boat – speed of stream.
$ \Rightarrow D.S = x + y$ Km/hr....................... (1)
And
$ \Rightarrow U.S = x - y$ Km/hr......................... (2)
Now as we know the relation of speed, distance and time which is
${\text{Speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$
Now it is given that downstream speed is 60 km in one and half hours or we can say in 1.5 hour.
$ \Rightarrow D.S = \dfrac{{60}}{{1.5}} = 40$ Km/hr.
And the upstream speed is 60 km in 2 hours.
$ \Rightarrow U.S = \dfrac{{60}}{2} = 30$ Km/hr.
Now from equations (1) and (2) we have,
$ \Rightarrow x + y = 40$........................... (3)
And
$ \Rightarrow x - y = 30$........................... (4)
Now add equation (3) and (4) we have,
$ \Rightarrow x + y + x - y = 40 + 30$
$ \Rightarrow 2x = 70$
$ \Rightarrow x = 35$ Km/hr.
Now substitute this value in equation (3) we have,
$ \Rightarrow 35 + y = 40$
$ \Rightarrow y = 40 - 35 = 5$ Km/hr.
So the speed of a race-boat in still water is 35 km/hr, and the speed of stream is 5 km/hr.
So this is the required answer.
Hence option (A) is correct.

Note – In this question the trick part was about the understanding of upstream and downstream, upstream is the direction towards the fluid source or this means that we are going in the opposite direction to the flow as the flow will be directed away from the source. Downstream means towards the direction in which fluid is going or away from the source. That’s why the speed of the boat is added with the speed of stream in downstream and subtracted in case of upstream.