Question

A ship, 40 km from the shore, springs a leak which admits 3 3/4 tonnes of water in 15 min. 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. \(1\frac{1}{2}\) km/h
• B. \(2\frac{1}{2}\) km/h
• C. \(3\frac{1}{2}\) km/h
• D. 2 km/h

Answer 1

The Correct Option is D

To find the average rate of sailing, we must determine how long it takes for the water level to reach 60 tonnes, as this is when the ship will sink. The ship is 40 km from the shore.

Step 1: Calculate the rate at which water enters the ship.
Water enters the ship at a rate of \( \frac{3.75 \text{ tonnes}}{15 \text{ min}} = \frac{3.75 \text{ tonnes}}{0.25 \text{ hr}} = 15 \text{ tonnes/hr} \).

Step 2: Calculate the effective rate at which water is leaving the ship.
The pumps can remove water at the rate of 12 tonnes/hr. Therefore, net water entering the ship is \( 15 - 12 = 3 \text{ tonnes/hr} \).

Step 3: Determine the time before the ship sinks.
The ship will sink when 60 tonnes of water is reached. Since we start with 0 tonnes, the time to reach 60 tonnes at the rate of 3 tonnes/hr is \( \frac{60 \text{ tonnes}}{3 \text{ tonnes/hr}} = 20 \text{ hours} \).

Step 4: Calculate the required average speed of the ship.
The ship needs to reach the shore in 20 hours. So, the average speed \( v \) needed is \( \frac{40 \text{ km}}{20 \text{ hr}} = 2 \text{ km/hr} \).

Final Answer: The average rate of sailing should be 2 km/h to reach the shore just as it begins to sink.