Trains A and B left stations R and S simultaneously on two s

Question

Trains A and B left stations R and S simultaneously on two seperate parallel rail tracks that are 350 miles long. The trains passed each other at point X after travelling for a certain amount of time. How many miles of the rail tracks had train A travelled when the two trains passed each other?

1) up to point X, the average speed of train B was 25% less than the average speed of train A.
2) up to point X, the average speed of train B was 60 mph and it took two and a half hours for train B to arrive at point X.

shameekv · Accepted Answer

First of all we have to make an inference here, that the 2 trains are running opposite to each other. Since they meet up at some point X. Otherwise they wouldn't have ever met if they ran in the same direction. Statement 1:- Let Speeds be B and A. Therefore B = \frac{3A}{4} Speed = \frac{Distance}{Time} A+B = \frac{350}{T} Lets take T as time taken by the trains to meet at point X. A+B is the effective speed of A and B. Therefore A+\frac{3A}{4} = \frac{350}{T} \frac{7A}{4} = \frac{350}{T} Therefore A = \frac{200}{T} Now A's distance will be Distance= Speed * Time i.e. Distance covered by A = \frac{200}{T} * T i.e. 200 hence Sufficient. Statement 2 :- Speed = \frac{Distance}{Time} A+B = \frac{350}{T} if we know B and we know T then we can get value of A from above equation. And then using Distance = Speed * Time (where time will again be two and half hours) we can calculate distance covered by A Hence Sufficient. Thus D is the answer. Drop some Kudos if the post helps!!! :-D

kusena · Answer

Distance between R and S is 350miles.

From stmt 1) Avg speed of B was 25% less than Avg speed of A
 Vb=(3/4)*Va
 Va/Vb=4/3 
Since the time traveled till point X being same for both the trains.Distance traveled will be in the same ratio as Speeds..i.e. 4:3
 
Distance traveled by A=(4/7)*350=200 miles...Hence stmt (1) alone is Sufficient

From stmt 2) Avg speed of B=60 miles and time taken is given as 2 1/2 hrs
 Total distance traveled by B =60*5/2=150 miles.So distance traveled by A will be 350-150=200 miles...Hence Stmt (2) alone is sufficient

Ans D

fozzzy · Answer

@shameekv great explanation... regarding the inference the latter portion of the question says they passed each other. so they are travelling towards each other.

How many miles of the rail tracks had train A travelled  when the two trains passed each other?

shameekv · Answer

Thanks!! I am not sure if you are asking me that question. Well A would have traveled 200 miles and B would have traveled 150 miles when the 2 trains passed each other as is derived in my post.

szhuge · Answer

Question should be reworded somehow to explicitly confirm that the parallel tracks' endpoints are R and S. From the statement you can only assume that one track starts at R, and one track starts at S and that they are parallel. It could be the case that the distance between R and S < 350 miles, so the track starting at S ends at a station beyond R, and the track starting at R ends at a station beyond S (I totally thought that was the trap in this question)

ScottTargetTestPrep · Answer

Since we have a converging problem, we can use the formula distance of train A + distance of train B = 350. Since both trains left the station at the same time, we can let each time = t.

Statement One Alone:

Up to point X, the average speed of train B was 25% less than the average speed of train A.

We can let the rate of train A = r and the rate of train B = 0.75r. We see that the distance of train A = rt and the distance of train B = 0.75rt. Thus:

rt + 0.75rt = 350

1.75rt = 350

rt = 200

Since rt = the distance for train A, train A had traveled 200 miles by the time it reached point X.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

Up to point X, the average speed of train B was 60 mph and it took two and a half hours for train B to arrive at point X.

Thus, train B travelled 60 x 2.5 = 150 miles when it reached point X. Recall that distance of train A + distance of train B = 350; train A must have travelled 200 miles by the time it reached point X.

Statement two alone is sufficient to answer the question.

Answer: D

giovannisumano · Answer

I think this question is flawed, it doesn't state if the trains are traveling in opposite directions. Before looking at the answers they way the question is stated opens a number of different scenarios, such as the trains travelling in the same direction without constant rates. An official question would never be stated like this, and I think a well done question should stick to official question rules.

CrackverbalGMAT · Answer

Distance between R and S is given as 350miles.

Statement 1:
 Average speed of B was 25% less than Average speed of A
Average Speed of A = Sa
Average Speed of B= Sb
Sb= Sa – 25% of Sa
Sb= Sa-1/4 Sa
Sb = (3/4) * Sa
Sa/Sb=4/3
Since the time taken by each train to reach meeting point X from starting point being the same.
Distance travelled will be in the same ratio as Speed i.e., 4:3
D1= S1*T Distance = Speed * time 
D2 = S2*T
Since T is constant, D1/D2 = S1/S2
So, in this case, Da/Db= 4/3

Distance travelled by A= Da= (4/7) *350=200 miles
Hence Statement 1 alone is Sufficient

Statement 2:
 The average speed of train B was 60 mph and time taken to reach meeting point is given as 2.5 hrs
Distance travel led by Train B to reach point X = 60* 2.5 = 150 miles.
So, Distance travelled by A = 350-150=200 miles
Hence Statement 2 alone is sufficient

Option D is the answer.

Thanks,
Clifin J Francis,
GMAT SME

bumpbot · Answer

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Trains A and B left stations R and S simultaneously on two s

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