Question

A leak was found in a ship when it was 77 km from the shore. The leak admits 2.25 tonnes of water in 5.5 minutes. 92 tonnes will suffice to sink the ship. The pumps can throw out water at 12 tonnes per hour. Find the average rate of sailing at which the ship may reach the shore as it begins to sink.

• A. 9.75 km/h
• B. 13 km/h
• C. 14.5 km/h
• D. 10.5 km/h

Hint:

In leakage and work–time problems, always compute: 1. Leak inflow rate, 2. Pump outflow rate, 3. Net filling rate, 4. Time to sink, and 5. Speed = distance/time.

Answer 1

The Correct Option is D

Step 1: Calculate the rate of water entering the ship (leak rate).
Leak admits 2.25 tonnes in 5.5 minutes.
Rate per minute = $\dfrac{2.25}{5.5} = 0.4091$ tonnes/min.
Converting to per hour: $0.4091 \times 60 \approx 24.55$ tonnes/hour.
Step 2: Net rate of water accumulation in the ship.
Pumps throw out water = $12$ tonnes/hour.
Net inflow = $24.55 - 12 = 12.55$ tonnes/hour.
Step 3: Time until the ship sinks.
Ship can hold $92$ tonnes before sinking.
Time to sink = $\dfrac{92}{12.55} \approx 7.33$ hours.
Step 4: Required average speed.
Distance to shore = $77$ km.
Time available = $7.33$ hours.
Speed required = $\dfrac{77}{7.33} \approx 10.5$ km/h.
Final Answer: The ship must travel at least \[ \boxed{10.5 \text{ km/h}} \] to just reach the shore in time.