A boat covers a certain distance downstream in 1 hour, while it comes back in 1¹/₂ hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?

112 kmph
213 kmph
314 kmph
415 kmph

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Let the speed of the boat in still water be x k m p h, then \\ Speed downstream \\ = (x + 3) k m p h \\ Speed upstream \\ = (x - 3) k m p h \\ ∴ (x + 3) \times 1 = (x - 3) \times \frac{3}{2} \\ \Rightarrow 2 x + 6 = 3 x - 9 \\ \Rightarrow x = 15 k m p h \end{aligned}

$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{speed}}\,{\text{of}}\,{\text{the}}\,{\text{boat}}\,{\text{in}}\,{\text{still}}\,{\text{water}}\,{\text{be}}\,x\,kmph{\text{,}}\,{\text{then}} \cr & {\text{Speed}}\,{\text{downstream}} \cr & = \left( {x + 3} \right)\,kmph \cr & {\text{Speed}}\,{\text{upstream}} \cr & = \left( {x - 3} \right)\,kmph \cr & \therefore \left( {x + 3} \right) \times 1 = \left( {x - 3} \right) \times \frac{3}{2} \cr & \Rightarrow 2x + 6 = 3x - 9 \cr & \Rightarrow x = 15\,kmph \cr}$