Question:
A motor boat covers a given distance in 6 hours moving down stream in a river. It covers the same distance in 10 hours moving upstream. The time it takes to cover the same distance in still water is:
A motor boat covers a given distance in 6 hours moving down stream in a river. It covers the same distance in 10 hours moving upstream. The time it takes to cover the same distance in still water is:
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Time in still water = $\frac{2 \times T_{up} \times T_{down}}{T_{up} + T_{down}}$? Wait, check the harmonic mean derivation: $t = \frac{2 t_1 t_2}{t_1 + t_2}$.
Updated On: Jun 6, 2026
- 6.5 hours
- 8 hours
- 9 hours
- 7.5 hours
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The Correct Option is D
Solution and Explanation
Step 1: Concept
Relative velocity in a river stream.
Step 2: Meaning
Calculating time in still water using upstream and downstream times.
Step 3: Analysis
Let the distance be $D$. Downstream velocity $v+u = D/6$. Upstream velocity $v-u = D/10$. Still water velocity $v = \frac{(D/6 + D/10)}{2} = \frac{16D/60}{2} = \frac{8D}{60} = \frac{2D}{15}$. Time in still water $= D/v = D / (2D/15) = 7.5$ hours.
Step 4: Conclusion
The time required is 7.5 hours.
Final Answer: (D)
Relative velocity in a river stream.
Step 2: Meaning
Calculating time in still water using upstream and downstream times.
Step 3: Analysis
Let the distance be $D$. Downstream velocity $v+u = D/6$. Upstream velocity $v-u = D/10$. Still water velocity $v = \frac{(D/6 + D/10)}{2} = \frac{16D/60}{2} = \frac{8D}{60} = \frac{2D}{15}$. Time in still water $= D/v = D / (2D/15) = 7.5$ hours.
Step 4: Conclusion
The time required is 7.5 hours.
Final Answer: (D)
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