Question

A motorboat, whose speed is $15$ km/hr in still water goes $30$ km downstream and comes back in a total of $4$ hours $30$ minutes. The speed of the stream is

• A. $4$ km/hr
  
• B. $6$ km/hr
  
• C. $10$ km/hr
  
• D. $5$ km/hr
  

Answer 1

The correct option is D $5$ km/hr


Let the speed of the stream be $x$ km/hr
Then,
Speed in downstream $=15+x$ km/hr
Speed in upstream $=15-x$ km/hr
and total time taken $=4.5$ hr
$\therefore \frac{30}{15+x}+\frac{30}{15-x}=4.5$
$\Rightarrow \frac{900}{225-x^2}=\frac{9}{2}$
$\Rightarrow 225-x^2=200$
$\Rightarrow x^2=25$
$\Rightarrow x=5,-5$(rejected)
$\therefore x=5$ km/hr