Train X departs Rockburg for Williamsland at 1:00 p.m. and

Thank you for your explain, actually I was wondering about the extracted equation from the two statements, I didn't get why when they cross each other, they both have completed 200 miles together??

shouldn't the equation be like this

2.5*50 = 1.5y------ because when they cross each other, then they both will have the same distance, but it also means that they didn't complete the whole distance, which is 200

X started out from R and Y started out from W. The distance between R and W is 200 miles. They met each other at 3:30. HOw much distance do they need to cover together to meet? They need to cover the original distance between them. What is the original distance between them? 200 miles. So they together covered 200 miles. That's how you get the equation.

Distance covered by X + Distance covered by Y = 200
(time of X * speed of X) + (time of Y * speed of Y) = 200
2.5*50 + 1.5 * Y = 200

Think, if you are your friend are 10 m apart and you want to meet, how many meters do you need to cover together? 10 M of course. It doesn't matter whether you cover 9 and he covers 1 or you cover 2 and he covers 8 etc. But together, you need to cover 10. It is not essential that you both need to cover equal distances. If you start at different times and/or if your speed is different, you will likely cover different distances. This is the same case.

You can actually do this equation using a diagram and without making any equation. I will explain it in a while.

This is what we know: Distance between X and Y initially is 200 miles. X starts at 1:00 pm and Y at 2:00 pm. We need to know the difference between speeds of X and Y.

(1) Train X arrives at Williamsland at 5:00 p.m.
We know the time taken by X to cover 200 miles but not the time taken by Y. So we cannot say what the difference between their speeds is.

(2) Train X and train Y pass each other at 3:30 p.m.
The two trains cross each other at 3:30. So X has traveled for 2.5 hrs and Y for 1.5 hrs and they have together covered 200 miles. But we don't know the individual distances covered by them and hence, we don't know their speeds. Think of it this way: say X is very slow. It could still start at 1:00 and meet at 3:30 if Y is very fast. On the other hand, if X is very fast, it could start at 1:00, meet at 3:30 (Y is slow) and reach the other side.

Now the problem is to figure out if together the two statements are sufficient. Note that they meet at 3:30 and X reaches the other side at 5:00 i.e. it takes 1.5 hrs to cover the remaining distance. This 'remaining distance' is the distance covered by Y when it started at 2:00 and met at 3:30 i.e. in 1.5 hrs. Basically, V=X and Y both covered the same distance in 1.5 hrs and hence their speeds are the same. So X has the same speed as Y.

I have made a diagram below to reinforce this.


Notice that Y travels on the green line and takes 1.5 hrs to do it. X travels from the meeting point to the other end (same as the distance of the green line) in 1.5 hrs. SO we can conclude that their speeds are the same.

Thank you very much guys you made it clear to me now, cheers

Train X departs R for W at 1:00 p.m. and train Y departs W for R at 2:00 p.m. If R and W are 200 miles apart, how much faster is train X than train Y ?
We are looking for the speed of train X vs. train Y.

Speed = distance/time
Distance = rate*time

(1) Train X arrives at Williamsland at 5:00 p.m.
This tells us that train X traveled for four hours. The average speed of X is therefore 50 miles/hour. Still, we know nothing about the speed of Y.
INSUFFICIENT

(2) Train X and train Y pass each other at 3:30 p.m.
Depending on the speed of X and Y, they could have passed one another at the midpoint or at some other point along the tracks. We know nothing of their speed.
INSUFFICIENT

Train X travels 2.5 hours and train Y travels 1.5 hours when they pass each other. When they do pass one another, they will have covered a total of 200 miles.
d1+d2=200
distance = r*t
d1: (50mph*2.5 hours)
d2: (s*1.5 hours+
total distance = 200
(50*2.5)+(s*1.5)=200
125+1.5s = 200
1.5s = 75
s = 50

The speed for both trains is the same, 50 miles/hour.
SUFFICIENT

(C)

(1) Simply gives the time of arrival of the first train heading to W. The time of arrival allows us to calculate the speed of 50 mph of X. As we know nothing about Y we are unable to answer the question.

(2) Given that they pass each other at 3:30 we see that X has traveled for 2,5h and Y has traveled for 1,5h. The total distance that they would have traveled together at this point is 200 miles.

2,5X+1,5Y=200. We are not able to solve this equation without additional information either about X, Y or the relation between X and Y and thus, we are unable to answer the question.

(1&2)
2,5X+1,5Y=200
X=50
-> 2,5*50+1,5Y=200
-> 1,5Y=75
-> Y = 50

Thus, X-Y = 0. They travel the same speed.

(Although, as this is a DS question one could stop without solving the equations above)

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