madimo wrote:
Train X departs Rockburg for Williamsland at 1:00 p.m. and train Y departs Williamsland for Rockburg at 2:00 p.m. If Rockburg and Williamsland are 200 miles apart, how much faster is train X than train Y ?
(1) Train X arrives at Williamsland at 5:00 p.m.
(2) Train X and train Y pass each other at 3:30 p.m.
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.
Attachment:
Ques3.jpg [ 8.4 KiB | Viewed 4696 times ]
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.
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