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

@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?

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.

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)

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

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.

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.