A boat can row a distance of 40 km down-stream and return in a total of 10 hours. If the speed of the boat in still water is five times that of the current, find the speed of the current?
1 km/hr
2 km/hr
2.75 km/hr
5/3 km/hr
Solution
Let the speeds of current and boat be $x$ and $5x$ respectively.
Time to go 40 km downstream $ = \frac {40}{5x +x } = \frac {40}{6x}$ hr.
Time to go 40 km upstream $ = \frac {40}{50-x} = \frac {40}{4x}$ hr.
Given, $\frac {40}{6x} + \frac {40}{4x} = 10 \Rightarrow \frac {1}{6x} + \frac {1}{4x} = \frac {10}{40}$
Multiply both sides by $12 x$, we get
$ 2 + 3 = 3x $ or $x = \frac {5}{3}$ km/hr.