Question

The distance between two points $A$ and $B$ is $16$ km. A boat makes a return journey from point $A$ to point $B$ and back in $5$ hours $36$ minutes. One way, it travels with the stream and on the return, it travels against the stream. If the speed of the stream increases by $2$ km/hr, then return journey takes $9$ hours $20$ minutes. What is the speed of the boat in still water?

• A. $5$ km/hr
• B. $3$ km/hr
• C. $7$ km/hr
• D. $9$ km/hr

Answer 1

The correct option is C $7$ km/hr

Let $x$ be the speed of boat upstream and $y$ be the speed of boat downstream.
Then, $\frac{16}{x}+\frac{16}{y}=\frac{28}{5}\cdots \left(1\right)$
and $\frac{16}{x-2}+\frac{16}{y+2}=\frac{28}{3}\cdots \left(2\right)$
Solving equations $\left(1\right)$ and $\left(2\right),$ we get
$x=4$ km/hr and $y=10$ km/hr
$\therefore$ Speed of boat in still water $=\frac{4+10}{2}=7$ km/hr