A ship develops a leak from the shore. Despite the leak, the ship is able to move towards the shore at a speed of . However, the ship can stay afloat only for . If a rescue vessel were to leave from the shore towards the ship and it takes to evacuate the crew and passengers of the ship, what should be the minimum speed of the rescue vessel in order to be able to successfully rescue the people aboard the ship?
- A65 km/hr
- B67 km/hr
- C68 km/hr
- D70 km/hr
Solution & Step-by-step Explanation
Step 1: Determine the available traveling time
The ship can stay afloat for a total of .
It takes for evacuation.
Therefore, the maximum time available for the ship and the rescue vessel to meet is:
Converting time into hours:
Step 2: Use the concept of Relative Speed
The ship and the rescue vessel are moving towards each other.
Let the speed of the rescue vessel be .
The speed of the ship .
The total distance between them initially is .
Hence, the minimum speed of the rescue vessel must be .
The ship can stay afloat for a total of .
It takes for evacuation.
Therefore, the maximum time available for the ship and the rescue vessel to meet is:
Converting time into hours:
Step 2: Use the concept of Relative Speed
The ship and the rescue vessel are moving towards each other.
Let the speed of the rescue vessel be .
The speed of the ship .
The total distance between them initially is .
Hence, the minimum speed of the rescue vessel must be .