Discussion Forum

A person can row a boat $d$ km upstream and the same distance downstream in 5 hours 15 minutes. Also, he can row the boat $2d $ km upstream in 7 hours. How long will it take to row the same distance $2d$ km downstream?

Answer:

Explanation:

Let the speeds of boat and stream be $x$ and $y$ km/hr respectively.

Then, Rate downstream $=(x+y)$ km/hr and Rate upstream $=(x-y)$ km/hr

Given $\frac{d}{(x+y)} +\frac{d}{( x-y )}$ $=5$ hrs $15$ minutes $=\frac{21}{4}$ hours

and $\frac{2d}{(x-y)}$ $= 7$ $=\frac{d}{(x-y)}$ $\frac{7}{2}$

$\Rightarrow\frac{d}{(x+y)}$ $=\frac{21}{4}-\frac{7}{2}$ $=\frac{7}{4}$

$\Rightarrow\frac{2d}{(x+y)}$ $=\frac{7}{2}$

Hence, he takes $\frac{7}{2}$ hours to row $2d$ km distance downstream.