Question

A ship, 40 km from the shore, springs a leak which admits \(3\dfrac{3}{4}\) tonnes of water in 15 minutes. 60 tonnes would suffice to sink her, but the ship's pumps can throw out 12 tonnes of water in one hour. Find the average rate of sailing, so that it may reach the shore just as it begins to sink.

• A. \(1\dfrac{1}{2}\) km/h
• B. \(2\dfrac{1}{2}\) km/h
• C. \(3\dfrac{1}{2}\) km/h
• D. 2 km/h

Hint:

Find net water inflow per hour, then time to reach 60 tonnes, then required speed.

Answer 1

The Correct Option is D

Step 1: Find the rates of water entering and leaving the ship.
The leak admits \(3\dfrac{3}{4}=\dfrac{15}{4}\) tonnes in 15 minutes. In 1 hour (4 times 15 minutes), it admits \(\dfrac{15}{4}\times4=15\) tonnes.
The pumps throw out 12 tonnes per hour.

Step 2: Find the net rate of accumulation.
Net gain \(= 15-12=3\) tonnes/hour.

Step 3: Find how long the ship can stay afloat.
The ship sinks once 60 tonnes have accumulated:
\[ \text{Time} = \frac{60}{3} = 20\text{ hours} \]

Step 4: Find the required average speed.
The ship must cover 40 km in exactly 20 hours:
\[ \text{Speed} = \frac{40}{20} = 2\text{ km/h} \]

Final Answer:
The ship must sail at an average rate of 2 km/h, so option D is correct. \[ \boxed{2\ \text{km/h}} \]