Time, speed and distance?

Question

A train X leaves Mumbai at 10 am and reaches Nashik at 1 pm. Train Y leaves Nashik at 11.30 am and reaches Mumbai at 2.00 pm.

At what time do the two trains cross one another?

Answer 1

They cross at 12:10:54.54 pm.

The assumption here is that the question is answerable.  In order for this question to be answerable, the trains HAVE to travel the same path (different tracks so they don't collide), and they have to travel at a constant speed.

What you have is that each train travels a total of D miles.

The speed of the X train is the total distance divided by the total time which is D/3.  The speed of the Y train is D/2.5.

The two trains pass each other at a point which is D-m miles from Mumbai.  The X train travels D-m miles.  The Y train, travelling in the other direction travels m miles.

The amount of time the X train travels to the rendezvous point is T.  Since the Y train leaves 1.5 hours later, it travels for T-1.5 hours to get to the same point.

Using the standard distance = rate times time formula, you have for the X train:

D - m = D/3 x T

for the Y train:

m = D/2.5 x (T-1.5)

Now solve for T (travel time for train X)

You have the two equations, so substitute the value of "m"

D - D/2.5 x (T-1.5) = D/3 x T

multiply through by 2.5, then by 3 to get rid of the fractions and:

2.5D - D (T-1.5) = 2.5DT/3

7.5D - 3D(T-1.5) = 2.5DT

7.5D - 3DT + 4.5D = 2.5DT

12D - 3DT = 2.5DT

add 3DT to each side:

12D = 5.5DT

Divide each side by D

12 = 5.5T

Divide each side by 5.5

2.181818 = T    (total time traveled by X train in hours)

Since T is the time the X train travelled, add that time (2 hours 10 minutes and 54 seconds) to 10 am to get the 12:10:54 passing time.

The Y train would have traveled for 1.5 hours less since it left at 11:30, one and a half hours after the X train...So...

the Y train would have traveled for 40 minutes and 54 seconds.

The actual distance travelled (and therefore the speed of each train) does not matter in this problem, but try it for 75 miles or 1000 miles and it will still be the same time of passage.

At 75 miles, the X train travels 25 miles an hour to make the trip in 3 hours.  The Y train travels at 30 miles an hour to make the trip.  After 2.1818 hours, the X train has gone 54.54 miles and the Y train, travelling for 1.5 hours less (.681818 hours) will have gone 20.45 miles.  The two trains together will have travelled 75 miles at 12:10:54.

Answer 2

Not enough information.  Are the tracks they are traveling on the same length?  Are the trains running at the same velocity?  Without more details, the only answer anyone can give is "sometime between 11:30 a.m. and 1:00 p.m."  Most likely somewhere near the middle (12:15 p.m.) of this, though.