Question:
A boat travels 36 km downstream in 3 hours and 24 km upstream in 3 hours. What is the speed of the boat in still water?
A boat travels 36 km downstream in 3 hours and 24 km upstream in 3 hours. What is the speed of the boat in still water?
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For boat and stream problems, set up downstream and upstream speed equations and solve simultaneously for the boat's speed.
Updated On: Jul 28, 2025
- 10 km/h
- 11 km/h
- 12 km/h
- 13 km/h
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The Correct Option is A
Solution and Explanation
- Step 1: Let the boat's speed in still water be $b$ km/h and the stream's speed be $s$ km/h.
- Step 2: Downstream speed = $b + s = \dfrac{36}{3} = 12$ km/h.
- Step 3: Upstream speed = $b - s = \dfrac{24}{3} = 8$ km/h.
- Step 4: Add the equations: $(b + s) + (b - s) = 12 + 8$, so $2b = 20$, $b = 10$ km/h.
- Step 5: Verify: If $b = 10$, then $s = 12 - 10 = 2$. Upstream: $10 - 2 = 8$ km/h, matches.
- Step 6: Check options: Option (a) is 10 km/h, which matches.
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