Question

A ship 156 km from the shore develops a leak which admits 2.5 metric tons of water in 6 minutes and 30 seconds. A quantity of 68 metric tons would suffice to sink the ship, but luckily the ship's pumps can throw out 15 metric tons in an hour. The average rate of sailing so that it just reaches the shore from where it left as it begins to sink should be:

• A. 25 kmph
• B. 10 kmph
• C. 18 kmph
• D. 15 kmph
• E. 60 kmph

Hint:

Net accumulation = Inflow rate - Outflow rate. Time = Total water / Net rate.

Answer 1

The Correct Option is C

Step 1: Calculating Inflow Rate:
Water inflow = 2.5 metric tons in 6 minutes 30 seconds = 6.5 minutes.
Inflow rate = \(\frac{2.5}{6.5}\) tons/minute.
Inflow per hour = \(\frac{2.5}{6.5} \times 60 = \frac{150}{6.5} = \frac{1500}{65} = \frac{300}{13} \approx 23.077\) tons/hour.

Step 2: Net Accumulation Rate:
Pump outflow = 15 tons/hour.
Net inflow = Inflow - Outflow = \(\frac{300}{13} - 15 = \frac{300 - 195}{13} = \frac{105}{13} \approx 8.077\) tons/hour.

Step 3: Time to Sink:
Water needed to sink = 68 tons.
Time to accumulate 68 tons = \(\frac{68}{105/13} = 68 \times \frac{13}{105} = \frac{884}{105} \approx 8.419\) hours.

Step 4: Required Speed:
Distance = 156 km.
Speed = \(\frac{156}{884/105} = 156 \times \frac{105}{884} = \frac{16380}{884} \approx 18.53\) kmph.
Closest is 18 kmph.