Boats X and Y are moving towards each other in still water. They recei

Question

Boats X and Y are moving towards each other in still water. They receive a warning just in time to avoid colliding into each other. Had they not received it, they would have collided in exact 2 minutes. Find the distance between them when they received the warning.

(1) The distance between the boats when they start moving towards each other is 10 Miles

(2) Boat X moves at a speed of 40 Miles/hr and Boat Y at 60 Miles/hr

GMATinsight · Answer

CONCEPT : Relative speed of two objects moving in opposite Direction = Sumk of their speeds

Relative speeds = x+y (if the speed of the boats X and Y are x and y respectively)

Question: Distance between Boats X and Y = Relative speed*Time of collision = (x+y)*2 = ?

Statement 1 : The distance between the boats when they start moving towards each other is 10 Miles

We do NOT know whethe rthey received warning immediately on start or after some time of their start hence

NOT SUFFICIENT

STatement 2 : Boat X moves at a speed of 40 Miles/hr and Boat Y at 60 Miles/hr

Now, we know the values of x and y each hence

SUFFICIENT

Answer: Option B

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • Let us assume that the d be the distance between the boats when they received the warning.
• We need to find d.
 o Now, d = speed of boat X (units/minute) * 2 + Speed of boat Y(units/minute) *2  
Thus, we can find d if we know speed of the two boats.
Keeping above analysis in mind let’s analyse each statement individually.
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  The distance between the boats when they start moving towards each other is 10 Miles
 • From this statement all we came to know is the initial distance between boat X and boat Y. 
 o However, we neither know their speed nor the time taken to reach the final point when they received the warning.  
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.
 Statement 2:  Boat X moves at a speed of 40 Miles/hr and Boat Y at 60 Miles/hr
 • This statement gives the speeds of the two boats. So, from here we can easily do the unit conversion of speed or time and calculate the value of d. 
Hence, statement 2 is sufficient.
Thus, the correct answer is  Option B.

sambitspm · Answer

This is a straightforward question. The distance between both the ships is to be calculated when they found out the warning.
Let's say distance is  x  and the speed of ships be  a  and  b  respectively.

GIven    = 2 minutes and x is required.

Clearly, if a and b are given, x can be calculated.

Answer -> B

poojakhanduja3017 · Answer

The answer is B

The concept which is used is : when two objects are moving, their relative speed can be calculated by seeing the direction in which they are moving. 
If they are moving towards each other, the relative speed is the maximum = a+b
As per the question, Distance,d between the boats when the warning is given = Speed (in this case, relative speed) * Time
 = (a+b) * 2 
Thus, if we have a and b, we can know d

Statement 1: The distance between the boats when they start moving towards each other is 10 Miles

We don't know the speeds, hence can't calculate based on this alone.  NOT SUFFICIENT

Statement 2: Boat X moves at a speed of 40 Miles/hr and Boat Y at 60 Miles/hr

Now, we know the values of a and b each . This statement is  SUFFICIENT

sujoykrdatta · Answer

From the problem stem: 
Distance between the boats when they receive the warning 
= Distance they would have combined covered in 2 minutes (= 2/60 hours)
= (S1 + S2) x (2/60)
where S1 and S2 are the speeds of the 2 boats in miles per hour

Why do we add?  
Since the boats approach each other, they would each come closer and the distance would be reduced by the sum of the distances they each approach towards each other (For example: if the gap between was 100 m and the boats approach 10 m and 20 m towards each other, the gap will reduce to 100 - 10 - 20 = 70 m)

Or, in other words, we can say that in opposite direction, relative speed is the sum of the speeds - the idea conveyed is the same!

Thus, it is clear that the value  (S1 + S2) * (2/60)  can be determined from Statement 2 (the information in Statement 1 is irrelevant)

Answer B

Boats X and Y are moving towards each other in still water. They recei

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