shanks2020 wrote:
akhilbajaj wrote:
Attachment:
Untitled.png
Distance between Washington (W) and Baltimore (B) = 120
Relative speed of trains A and B = 30+90=120
Therefore,
the trains together cover a distance of 120 miles in 1 hr and thus meet every hour.
At 1 hr, Train A travels 30 miles from W, Train B travels 90 miles from B. This is where the two trains meet (meeting pt 1).
At 2 hr, Train A reaches 60 miles from W, Train B travels 30 miles to W, turns around in negligible time and reaches 60 miles from W. This is where the two trains meet (meeting pt 2).
Distance between meeting pt 1 and pt2 = 60-30 = 30.
Answer B.
press kudos if the graphical representation helps you understand better!
How do we know they will be meeting every 1 hour?
Good question,
shanks2020. I have taken the liberty of highlighting the original text that states as much. If we picture each train on a parallel track, shuttling back and forth from city to city (although who would ever want to take the slow train?), we can model the position of each train per hour to test the statement. I am going to use color to make the graphical interpretation a bit easier on the eyes. Each
highlighted portion will represent a meeting of the two trains. I will also use an arrow (--> or <--) to indicate the number of 30-mile movements of each train per hour, as well as the direction of travel.
Train A (moves at 30 mph)
0---30--60---90---120 miles
|----|----|----|----|
Train B (moves at 90 mph)
120-90--60---30---0 miles
|----|----|----|----|
Again, the
question states that
the station turnaround times are negligible, so we can, for the sake of our simulation, assume constant motion. We must also ignore the rates at which each train would accelerate/decelerate, but with all of that said, let us take a look from the top:
Hour 1:
A:
|----|----|----|----| -->
B: |----
|----|----|----| <-- <-- <--
Hour 2:
A: |----|
----|----|----| -->
B:
|----|----|----|----| <-- --> -->
Hour 3:
A: |----|----|
----|----| -->
B: |----|----|
----|----| --> --> <--
Hour 4:
A: |----|----|----|
----| -->
B:
|----|----|----|----| <-- <-- <--
As you can see, after 4 hours of travel, the two trains will be in opposite cities at the same time, and it would not be until hour 5 that they would cross paths again and repeat the mirror of the hour 1 position:
Hour 5:
A: |----|----|----
|----| <--
B: |
----|----|----|----| --> --> -->
Thus, we can conclude that the trains will
not meet every hour under the given conditions. Of course, this meta-analysis does not help at all with the problem at hand, but it does correct an assumption, the type that could get a test-taker into trouble on another (similar) question, and I hope it satisfies your curiosity.
Good luck with your studies, and thank you for opening the door to my light-hearted response. (I miss physics schematics.)
- Andrew
Even we have to do a similar analysis till the faster turns around.
Maybe Bunuel has a faster and direct way to tell something about the meeting points after the 1st meeting point. The least what i can think of is that we will have to find manually till the second meeting and then we can draw some pattern, based on the combined distance covered to meet once.