Question

A motorboat goes down stream in a river and covers the distance between two coastal towns in five hours. It covers this distance upstream in six hours.

If the speed of the stream is $2$ km/hour, then find the speed of the boat in still water.

Answer 1

Since we have to find the speed of the boat in still water, let us suppose that it is $x$ km/h.
This means that while going downstream the speed of the boat will be $(x+2)$ kmph because the water current is pushing the boat at $2$ kmph in addition to its own speed '$x$' kmph.
Now the speed of the boat down stream $=(x+2)$ kmph
$\Rightarrow$ distance covered in $1$ hour $=x+2$ km
$\therefore$ distance covered in $5$ hours $=5(x+2)$ km
Hence the distance between $A$ and $B$ is $5(x+2)$km
But while going upstream the boat has to work against the water current.
Therefore its speed upstream will be $(x-2)$ kmph.
$\Rightarrow$ Distance covered in $1$ hour $=(x-2)$ km
Distance covered in $6$ hours $=6(x-2)$ km
$\therefore$ distance between $A$ and $B$ is $6(x-2)$ km
But the distance between $A$ and $B$ is fixed
$\therefore$ $5(x+2)=6(x-2)$
$\Rightarrow$ $5x+10=-12-10$
$\therefore$ $-x=-22$
$x=22$
Therefore speed of the boat in still water is $22$ kmph.