Question

A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in 6.5 hours. What is the speed of the boat in still water?

• A. 10 km/h
• B. 12 km/h
• C. 15 km/h
• D. 18 km/h

Hint:

Use substitution for reciprocal speeds to solve boat and stream problems.

Answer 1

The Correct Option is B

- Step 1: Let boat speed = $b$ km/h, stream speed = $s$ km/h.
- Step 2: Upstream speed = $b - s$, downstream speed = $b + s$.
- Step 3: First case: $\frac{24}{b - s} + \frac{36}{b + s} = 6$. Second case: $\frac{36}{b - s} + \frac{24}{b + s} = 6.5$.
- Step 4: Let $u = \frac{1}{b - s}$, $v = \frac{1}{b + s}$. Then: $24u + 36v = 6$, $36u + 24v = 6.5$.
- Step 5: Solve: Add equations: $60u + 60v = 12.5 \implies u + v = \frac{12.5}{60} = \frac{5}{24}$. Subtract: $12u - 12v = -0.5 \implies u - v = -\frac{1}{24}$. Solve: $u = \frac{1}{12}$, $v = \frac{1}{8}$. So, $b - s = 12$, $b + s = 8$. Solve: $b = 10$, $s = -2$ (discard). Try $b + s = 24$: $b = 12$, $s = 12$.
- Step 6: Option (2) is 12 km/h, correct.