Question

A boat takes $90$ minutes less to travel $36$ km downstream than to travel the same distance upstream. If the speed of the boat in still water is $10$ km/hr, then what is the speed of the stream ?

• A. $4$ km/hr
• B. $3$ km/hr
• C. $2.5$ km/hr
• D. $2$ km/hr

Answer 1

The correct option is D $2$ km/hr

Let the speed of the stream be $x$ km/hr.
Speed of boat in still water $=10$ km/hr
$\therefore$ Speed of boat downstream $=(10+x)$ km/hr
Speed of boat upstream $=(10-x)$ km/hr
Given, $\frac{36}{(10-x)}-\frac{36}{(10+x)}=\frac{90}{60}$
$\Rightarrow \frac{36(10+x)-36(10-x)}{(10-x)(10+x)}=\frac{3}{2}$
$\Rightarrow \frac{72x}{100-x^2}=\frac{3}{2}$

$\Rightarrow$ $144x=300-3$ $x^2$
$\Rightarrow 3x^2+144x-300=0$
$\Rightarrow 3x^2+150x-6x-300=0$
$\Rightarrow 3x(x+50)-6(x+50)=0$
$\Rightarrow (3x-6)(x+50)=0$
$\Rightarrow$ $x=2$ or $x=-50$
Since speed is not negative, $x=2$ km/hr.