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Quite Simple.... Washington to Baltimore - 120kms A takes 30mph B takes 90mph A at Washington and B at Baltimore at same time
at 1st hr, they meet for the first time, A would have covered 30kms from Washington, B 90kms from Baltimore at 2nd hr, they meet again, A would have covered 60kms from Washington, B would have covered 30kms from their first meeting point to Washington and then travels return journey of 60kms to meet at 60Kms point from Washington.
So first was at 30kms from Washington and 2nd was at 60kms from Washington...hence the difference is 30kms
Hope this is a simple method...but my worry is the more complex problems of this nature....can somebody share such problems?
Note: Give me kudos if my approach is right , else help me understand where i am missing.. I want to bell the GMAT Cat
Train speeds: Train A 30mph, Train B 90mph. Total distance is 120 miles. in 1st hour, train A would have travelled 30 miles, train B would have travelled 90 miles.
I st hour: Train A ---------> 30 miles <----------------------------- Train B 90 miles Train A and B meet at 30 miles.
2nd hour: train A would have another travelled 30miles, train B would have travelled another 90 miles.(remaining 30 miles and 60 miles on return)
Train A --------->------------> 60miles ----------------------> Train B 60miles second time, they meet at 60 miles. Difference in miles between the point they met at first time and second time is 60-30= 30 miles
Since Train A starts from Washington and Train B from Baltimore, hence they are travelling in opposite direction. So the relative speed = 120 mph (90 + 30).. Total time taken = Total distance / Relative speed => 120 / 120 = 1hr.
So the distance travelled by each train is : A - 30 miles ; B - 90 miles. Let this point of first rendevouz be X. Now the catch in the question is that they travel continuously, so there is a possibility that they may meet again while travelling in the same direction.. figure below: Washisngton .............X............Y........... Baltimore 30m 30m 30m
Now we can observe that while Train A would had travelled another 30 miles in next 1hr (its speed is 30 mph). So it’s distance from Washington = 60 miles. Train B would had covered the remaining 30 miles from X till Washington and backtracked to the current position of Train A by covering remaining 60m from Washington within 1 hr (train B speed is 90mph). Let this point of second meet be Y. So the distance between Y and X = 60 – 30 = 30 miles
-- Because beauty Lies in the Eyes.. So donate those eyes
For distance =120 and 2 trains at 90+30 mph= 120mph makes it very easy. For 1st time they will meet at 30miles from Washington..now from this moment we check when will they meet again, again the distance between them is 120 so again train A will meet after 30miles.
So in every one hour both trains will meet i.e. After 1 hour Train A reaches to a place C= 30 km from washington After 2 hour Train A reaches to a place D= 60 km from washington, Distance Between C and D = 30 After 3 hour Train A reaches to a place E= 90 km from washington, Distance Between D and E = 30
Do let me know in case there is a hole in the logic