Question

A ship developed a leak $15km$ from the shore and yet could travel towards the shore at a speed of $10km/hr$ for a maximum time of $18min$. A rescue vessel that was immediately sent from the shore to rescue the passengers would take $6min$ to complete the rescue once it reaches the ship. What should be the minimum speed of the rescue vessel in order to be able to successfully evacuate everyone onboard the ship?

Answer 1

Distance between ship and shore $=15km$

Velocity of ship $=10kmph$

Maximum time that the ship has $=18min$

As the rescue vessel will have 6 minutes to evacuate the ship, so the ship has $=18-6=12minutes$

So the rescue vessel must head up to the sinking ship in 12 minutes in order to make the rescue mission successful.

Let the speed of rescue vessel is 'x' kmph

Relative speed of the vessel and ship $=(10+x)kmph$ [as moving in different direction]

We know that

$\Rightarrow Relativespeed=\frac{Distance}{Time}$

$\Rightarrow (10+x)=\frac{15\times 60}{12}=75$

$\Rightarrow x=75-10$

$\Rightarrow x=65$

Therefore, rescue vessel must head with a minimum speed of 65 kmph.