Question

A steamer goes downstream and covers the distance between two ports in $4$ hours while it covers the same distance upstream in $5$ hours. If the speed of the stream is $2$ km/h, find the speed of the steamer in still water.

• A. $12$ km/hr
• B. $31$ km/hr
• C. $18$ km/hr
• D. $15$ km/hr

Answer 1

The correct option is C $18$ km/hr

Let the speed of the steamer in still water be $x$ km/h.

Then, the speed downstream $=(x+2)$ km/h
and the speed upstream $=(x-2)$ km/h

Given, distance covered in $4$ hours downstream $=$ distance covered in $5$ hours upstream
$\therefore 4(x+2)=5(x-2)$
$\Rightarrow 4x+8=5x-10$

$⟹4x-5x=-10-8$

[Transposing $5x$ to LHS and $8$ to RHS]

$⟹-x=-18$ or $x=18$km/h