Question

A boat running upstream takes $8$ hours $48$ min to cover a certain distance, while it takes $4$ hours to cover the same distance running downstream. What is the ratio between the speed of the boat and the speed of the water current respectively?

• A. $2:1$
• B. $3:1$
• C. $8:3$
• D. $4:3$

Answer 1

The correct option is C $8:3$

Let the distance covered in one direction be $x$ km.
Then, speed upstream $=$ $\frac{x}{\frac{44}{5}}$ km/hr
( $8$ hrs $48$ min $=$ $8\frac{48}{60}=8\frac{4}{5}hrs$)
$=$ $\frac{5x}{44}$ km/hr
Speed downstream $=$ $\frac{x}{4}$ km/hr
$\therefore$ Speed of boat in still water = $\frac{1}{2}(\frac{5x}{44}+\frac{x}{4})$
$=$ $\frac{8x}{44}=\frac{2x}{11}$ km/hr
Speed of current $=$ $\frac{1}{2}(\frac{x}{4}-\frac{5x}{44})=\frac{3x}{44}$ km/hr
$\therefore$ Required ratio $=$ $\frac{2x}{11}:\frac{3x}{11}=8:3$