A ship develops a leak 12 km from the shore. Despite the leak, the shi

Question

A ship develops a leak 12 km from the shore. Despite the leak, the ship is able to move towards the shore at a speed of 8 km/hr. However, the ship can stay afloat only for 20 minutes. If a rescue vessel were to leave from the shore towards the ship and it takes 4 minutes 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?

A. 53 km/hr
B. 44 km/hr
C. 37 km/hr
D. 28 km/hr
E. 26 km/hr

A. 53 km/hr
B. 44 km/hr
C. 37 km/hr
D. 28 km/hr
E. 26 km/hr

Archit3110 · Answer

good question took me a while , if anyone has someother solution then please share...

speed of ship 8 km /hr
since we have only 20 mins available & it takes 4 mins to rescue people + staff

so lets assume that ship will continue to sail towards shore for 16 mins 
distance covered in 16 mins would be 
d= 8 * 16/60 = 2.13 kms

distance left from shore 12-2.13 = 9.86 kms

let 9.86 km be the distance that rescue boat has to cover to reach out to ship

so time it would take has to be close to 16 mins..

lets plug in values from answer choices

option B 44 km/hr it time to cover 9.86 kms ; 9.86*60/ 44 = ~ 13.44 mins which is too fast

option C 37 km/hr , time to cover 9.86 kms ; 9.86*60/37 = 16 mins .. which is exact

IMO C is correct...

GMATinsight

sir the method i did to solve this question is too calculation intensive, please advise on a short cut method.. I think this question can also be solved using relative speed as well, but i was not able to equate the two eqns for both boats.. please check...

GMATinsight · Answer

Since ship can travel for 20 minutes and it takes 4 minutes to evacuate so the rescue team should arrive after 16 minutes from now

Distance travelled by ship in 16 minutes = 8*(16/60) = 32/15 km

i.e. Distance to be travelled by Rescue ship = 12 - (32/15) = 148/15 km

But rescue ship has only 16 minutes to cover this distance, therefore speed of rescue ship = (148/15)/(16/60) = 37 km/hr

Answer: Option C

Archit3110

Archit3110 · Answer

GMATinsight  :

sir i have solved the question using same steps its too calculation intensive .. I actually wanted to know whether this question can have an alternate solution like using equations considering relative speeds of both rescue boat and ship?
I actually tried but couldnt form an equation ...

dave13 · Answer

Speed of drowning boat \frac{8}{60} Speed of rescue boat is \frac{x}{60} Since both objects are moving towards each other add the speeds So their relative speed = \frac{8}{60} + \frac{x}{60} = \frac{8+x}{60} Time when they meet each other distance (12) divided by their relative speed 12 / (8+x)/60 = \frac{720}{8+x} The objects need to meet in 16 minutes, because it takes 4 minutes for rescue team to save the passengers = \frac{720}{8+x} = 16 = 720 = 16 (8+x) = 720 = 128+16x = 720- 128 = 16x = 16x = 592 x = 37 IMO: C

Gladiator59 · Answer

Here is how I did the math on this one.

Let the speed of rescue ship be x kmph.  Since the leaking ship will be able to travel for only 16 mins towards shore, the rescue ship will also have only 16 mins to reach the leaking ship.

Since both the ships are travelling towards each other, their relative speed would be (x + 8) kmph

And total distance travelled by both will be 12 km. So the math becomes a bit easier.

Speed * Time = Distance.

(x+8)*16/60 = 12
x + 8 = 15*3
x + 8 = 45
x = 45 - 8 = 37

Hence  Option (C) is our bet.

Best,
Gladi

hunter2000 · Answer

An easier way is using the formula

D/s1 + s2

so ,

12/8+x = 16/60
45= 8 + x
37 = x
so answer is c

GMATGuruNY · Answer

The ship can stay afloat for 20 minutes.
Since 4 of these 20 minutes are needed to evacuate the crew and passengers, the rescue vessel and the ship must meet in 16 minutes, the equivalent of 4/15 of an hour.

Since the ship and the rescue vessel travel toward each other, they WORK TOGETHER to cover the 12 kilometers between them.
For 12 kilometers to be traveled in 4/15 of an hour, the required rate  = \frac{distance}{time} = 12 ÷ \frac{4}{15} = 45  kilometers per hour.
Since the ship travels 8 kilometers eacb hour -- the ship and the rescue vessel together must travel 45 kilometers each hour -- the rate required by the rescue vessel = 45-8 = 37 kilometers per hour.

C

ScottTargetTestPrep · Answer

Solution:

Since the ship can stay afloat for only 20 minutes, and it takes 4 minutes to evacuate the crew and passengers of the ship, it can travel for only 16 minutes. Therefore, it can travel at most 8 x 16/60 = 32/15 km, which means it will be 12 - 32/15 = 148/15 km from the shore. Since the rescue vessel can also travel for 16 minutes, it needs to travel at least (148/15) / (16/60) = 148/15 x 60/16 = 37 km/hr. C is the correct answer.

Answer: C

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A ship develops a leak 12 km from the shore. Despite the leak, the shi

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