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A ship is 40 km away from shore. There is a hole in the ship from which \(\frac{{15}}{4}\) tons of water come in the ship in every 12 mins. There is another outlet tap that throws out 12 tons of water every hour. Find at what speed it should move such that when it begins to sink a rescue ship moves with 2 km/hr escapes the passengers of the ship if 60ton of water is enough to sink?

A ship is 40 km away from shore. There is a hole in the ship from which \(\frac{{15}}{4}\) tons of water come in the ship in every 12 mins. There is another outlet tap that throws out 12 tons of water every hour. Find at what speed it should move such that when it begins to sink a rescue ship moves with 2 km/hr escapes the passengers of the ship if 60ton of water is enough to sink? Correct Answer 2.5 km/hr

Given:

Leak admits 15/4 ton of water in every 12 min.

Ship is 40 km from the shore = Distance

An outlet tank can throw out 12 tons of water per hour

Speed of rescue ship = 2 km/hr

Formula used:

Speed = Distance/Time

Calculation:

15/4 ton of water in 12 min

∴ In 1 hour leak admits = 75/4 ton

An outlet tank can throw out 12 tons of water per hour

Every hour net water admit = (75/4) - 12 = 27/4 ton

27/4 ton water in = 1 hour

∴ 1 ton water = 4/27 hour

60 ton water in = 60 × (4 /27) = 80/9 hours

Let say speed of ship = s km/hour

Speed of rescue ship = 2 km/hour

Effective speed = (s + 2) km/hour

⇒ (s + 2) × (80/9) = 40 km (∵ Distance = speed × time)

⇒ 2s + 4 = 9

⇒ s = 5/2 = 2.5 km/hour

∴ It should move at the speed of 2.5 km/hour

 

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