Question

A stream goes downstream from one port to another in $4$ hours. It covers the same distance upstream in $5$ hours. If the speed of the stream is $2$ km/hr, the distance between the two ports is

• A. $50$ km
• B. $60$ km
• C. $70$ km
• D. $80$ km

Answer 1

The correct option is D $80$ km

Let the distance between the two parts be $x$ km.
Then, speed downstream $=$ $\frac{x}{4}$ km/hr
and speed upstream $=$ $\frac{x}{5}$ km/hr
$\Rightarrow$ Speed of stream $=$ $\frac{1}{2}(\frac{x}{4}-\frac{x}{5})$
Given, $\frac{1}{2}(\frac{x}{4}-\frac{x}{5})=2$

$\Rightarrow$ $\frac{x}{4}-\frac{x}{5}=4$

$\Rightarrow \frac{x}{20}=4$

$\Rightarrow x=80$ km