A boat covers 6 km in an hour in still water. It takes thrice as much time in covering the same distance against the current. What is the speed of the current? $ (a){\text{ 2km/hr}} \\ (b){\text{ 3km/hr}} \\ (c){\text{ 4km/hr}} \\ (d){\text{ 5km/hr}} \\ $
ANSWER
Verified
Hint – In this question let the speed of the boat in still water be x km/hr and speed of boat in current be ykm/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 solution - Let the speed of the boat 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 boat + speed of current. And the upstream (U.S) speed = speed of boat – 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 ${\text{Speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$ Let us consider that the distance which covered by the boat be (z) km and let the time taken to cover the distance with the current be (t1) hours and against the current be (t2) hours. $ \Rightarrow D.S = \dfrac{z}{{{t_1}}}$ Km/hr. And the upstream speed is 4 km in 2 hours. $ \Rightarrow U.S = \dfrac{z}{{{t_2}}}$ Km/hr. $ \Rightarrow D.S\left( {{t_1}} \right) = U.P\left( {{t_2}} \right)$..................... (3) Now it is given that the boat takes thrice as much time in covering the same distance against the current. $ \Rightarrow {t_2} = 3{t_1}$ So from equation (3) we have, $ \Rightarrow D.S\left( {{t_1}} \right) = U.P\left( {3{t_1}} \right)$ $ \Rightarrow D.S = 3\left( {U.S} \right)$ Now from equation (1) and (2) we have, $ \Rightarrow x + y = 3\left( {x - y} \right)$ Now simplify the above equation we have, $ \Rightarrow 3x - x = y + 3y$ $ \Rightarrow 4y = 2x$ Now divide by 4 we have, $ \Rightarrow y = \dfrac{{2x}}{4} = \dfrac{x}{2}$ Km/hr.......................... (4) Now it is given that a boat covers 6 km in an hour in still water. So the speed of the boat in still water, x = 6 km/hr. Now from equation (4) we have, $ \Rightarrow y = \dfrac{x}{2} = \dfrac{6}{2} = 3$ Km/hr. So this is the required answer. Hence option (B) 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 current in downstream and subtracted in case of upstream.