Question

Ritu can row downstream 20km in 2 hours, and upstream 4km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Answer 1

Hint: In this question let the speed of Ritu in still water be x km/hr and in current be y km/hr. Find the upstream and downstream speed in terms of variables and use the relation between distance, time and speed, to get the answer.

Complete step-by-step answer:
Let the speed of Ritu in still water be x km/hr.

And the speed of the current be y km/hr.

So the downstream (D.S) speed = speed of Ritu + speed of current.

And the upstream (U.S) speed = speed of Ritu – speed of current.

$ \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 20 km in 2 hours.

$ \Rightarrow D.S = \dfrac{{20}}{2} = 10$ Km/hr.

And the upstream speed is 4 km in 2 hours.

$ \Rightarrow U.S = \dfrac{4}{2} = 2$ Km/hr.

Now from equations (1) and (2) we have,

$ \Rightarrow x + y = 10$........................... (3)

And

$ \Rightarrow x - y = 2$........................... (4)

Now add equation (3) and (4) we have,

$ \Rightarrow x + y + x - y = 10 + 2$

$ \Rightarrow 2x = 12$

$ \Rightarrow x = 6$ Km/hr.

Now substitute this value in equation (3) we have,

$ \Rightarrow 6 + y = 10$

$ \Rightarrow y = 10 - 6 = 4$ Km/hr.

So the speed of Ritu in still water is 6 km/hr, and the speed of current is 4 km/hr.

So this is the required answer.

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 an individual is added with the speed of current in downstream and subtracted in case of upstream.