Question

A boat covers a certain distance between two spots on a river taking ‘ \[{t_1}\] ’ time on going down the stream and ‘ \[{t_2}\] ’ time going upstream, what time will be taken by the boat to cover the same distance in still water?
(A) \[\dfrac{{{t_1} + {t_2}}}{2}\]
(B) \[\dfrac{{{t_1}}}{2} + \dfrac{3}{4}{t_2}\]
(C) \[\dfrac{{2{t_1}{t_2}}}{{{t_2} + {t_1}}}\]
(D) \[\dfrac{{{t_2} + {t_1}}}{{2{t_1}{t_2}}}\]

Answer 1

Hint This is a simple question; we need to assume speed of water and then make two equations from it. First case when we are flowing upstream and second when we are going downstream. Now we have equations; using substitution we can easily calculate the time required by boat in still water.

Complete step-by-step answer:
Let the velocity of boat in still water be \[u\]
Velocity of water stream be \[v\]
Distance be \[d\]
Upstream time \[{t_1}\]
Downstream time \[{t_2}\]
Equation while going upstream
\[u + v = \dfrac{d}{{{t_1}}}\] -(1)
Equation while going downstream
\[u - v = \dfrac{d}{{{t_1}}}\] -(2)
Adding eq. 1 and 2
\[2u = \dfrac{d}{{{t_1}}} + \dfrac{d}{{{t_2}}}\]
\[u = \dfrac{{2{t_1}{t_2}}}{{{t_1} + {t_2}}}\]

Hence option C is correct.

Note Whenever you are asked to calculate the average speed, then you can calculate it with lay man’s concept which is total distance travelled divided by total time. And average velocity by total displacement divided by total time. Average velocity after travelling some distance can be zero but average can’t be zero.