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

Here is a second way, working entirely in minutes instead of converting to an hourly rate first.

1. Leak rate per minute. $3.75$ tonnes in 15 minutes is $3.75/15=0.25$ tonnes per minute.
2. Pump rate per minute. $12$ tonnes in 60 minutes is $12/60=0.2$ tonnes per minute.
3. Net rate per minute. $0.25-0.2=0.05$ tonnes per minute, net.
4. Time to reach 60 tonnes. $60/0.05=1200$ minutes $=20$ hours, matching the hourly calculation.
5. Required speed. The ship must travel 40 km in 20 hours: $40/20=2$ km/h.

Working in minutes gives the same 20-hour window and the same required speed, confirming option D. \[ \boxed{2\ \text{km/h}} \]