If the ratio of boat speed in still water to stream speed is $5:1$ and the boat travels $48$ km upstream in $3$ hours less than $144$ km downstream, then the speed of the boat in still water is:

Question

If the ratio of boat speed in still water to stream speed is $5:1$ and the boat travels $48$ km upstream in $3$ hours less than $144$ km downstream, then the speed of the boat in still water is:

Option A

16 km/h

Option B

18 km/h

Option C — Correct answer

20 km/h

Correct choice.

Option D

24 km/h

Explanation

Let still-water speed $=5x$ and stream speed $=x$. Then upstream and downstream speeds are $4x$ and $6x$. The condition gives $\frac{48}{4x}=\frac{144}{6x}+3$, so $\frac{12}{x}=\frac{24}{x}+3$ is incorrect in sign; interpret as downstream takes 3 hours less than upstream: $\frac{48}{4x}=\frac{144}{6x}-3$. This gives $\frac{12}{x}=\frac{24}{x}-3$, so $x=4$ and still-water speed $=20$ km/h.

Chapter Mock 9: Boat and Stream