Question

A ship developed a leak 15 km from the shore and yet could travel towards the shore at a speed of 10 km/hr for a maximum time of 18 min. A rescue vessel that was immediately sent from the shore to rescue the passengers would take 6 min 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?
1. 72 km/hr
2. 70 km/hr
3. 68 km/hr
4. 65 km/hr

Answer 1

Correct Answer - Option 4 : 65 km/hr

Given: 

Distance between ship and shore =15 km

Speed of ship =10 km/hr

The maximum time that the ship has to travel towards the shore = 18 min

Concept Used :

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

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

Formula Used:

Relative speed = Distance/Time

Calculations:
Let the speed of rescue vessel is x km/hr

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

We know that,

⇒ Relative speed = Distance/Time

⇒(10+x) = 15 × 60/12

⇒(10+x) = 75

⇒x = 75 − 10

⇒x = 65

∴ The rescue vessel must head with a minimum speed of 65 km/hr.