Question:
A ship 55 km from the shore springs a leak which admits 2 tonnes of water in 6 min; 80 tonnes would sink her, but the pumps can throw out 12 tonnes an hour. Find the average rate of sailing so that she may just reach the shore as she begins to sink.
A ship 55 km from the shore springs a leak which admits 2 tonnes of water in 6 min; 80 tonnes would sink her, but the pumps can throw out 12 tonnes an hour. Find the average rate of sailing so that she may just reach the shore as she begins to sink.
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For inflow-outflow problems, always compute the net rate first, then relate total allowable volume to time and speed.
Updated On: Mar 24, 2026
- 5.5 km/h
- 6.5 km/h
- 7.2 km/h
- 8.5 km/h
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The Correct Option is A
Solution and Explanation
Rate of water intake = \( \frac{2}{6} \times 60 = 20 \ \text{tonnes/hour} \).
Rate pumped out = \(12 \ \text{tonnes/hour}\).
Net rate of filling = \(20 - 12 = 8 \ \text{tonnes/hour}\).
Capacity before sinking = \(80 \ \text{tonnes}\).
Time to sink = \(80 / 8 = 10 \ \text{hours}\).
Speed needed = \(55 / 10 = 5.5 \ \text{km/h}\).
Rate pumped out = \(12 \ \text{tonnes/hour}\).
Net rate of filling = \(20 - 12 = 8 \ \text{tonnes/hour}\).
Capacity before sinking = \(80 \ \text{tonnes}\).
Time to sink = \(80 / 8 = 10 \ \text{hours}\).
Speed needed = \(55 / 10 = 5.5 \ \text{km/h}\).
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