To & Fro Motion Concept

Question

Hello,

I have been searching for material on To & Fro Motion but could not find what I needed. Any help is appreciated.

To & Fro Motion questions are generally approached with the assumption that after meeting once, the two bodies will reach the opposite ends, turn around and meet again. My question is, what if the assumption fails?
What if the speed of first body is high enough to reach the end, turn around and meet the second body even before the second body has reached its end?

For example, A and B start from opposite ends. After their first meet, A reaches the end, turns around and passes B before B has reached the end. I have represented the case below.

1st meet:
|------------>-------------------->A
__________________________B<-------|

2nd meet:
|------------->----------------------------->---|
___________________A<--------------<--|
___________________B<---------<-------|

How do we identify such cases?
What is the best approach for To & Fro Motion questions that takes such cases into account?

Thanks,

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MahmoudFawzy · Answer

Hi  Shadwal , I understand your concern.
Anyway, the difficulty of a question usually depends on the number of unknown you have to calculate, so I can't answer your question directly.
Second, I went through several distance-time questions, and I met this type to multilayered question from sources outside the official guide (so it is less likely to see this kind in real GMAT because it usually consumes too much time to solve in only 2 to 3 min.)

Here is some questions that I went through and are related to the concept you are discussing, please try them and we can use them as a starting point for further discussion if you need.
 https://gmatclub.com/forum/two-buses-p-and-q-start-from-cities-a-and-b-towards-each-other-they-m-251829.html#p1947353 
 https://gmatclub.com/forum/bus-1-and-bus-2-run-between-cities-a-and-b-216570.html#p1671852 
 https://gmatclub.com/forum/two-persons-a-and-b-start-from-the-opposite-ends-of-a-450-km-straight-309636.html#p2395909

ccooley · Answer

I understand your concern here, but the only valid answer here is "it depends on what the text of the problem says." If a GMAT problem uses this concept (and that's unlikely, unless it's an extremely difficult problem), then the problem will have to either avoid that situation, or make it completely clear what you're supposed to do in that situation.

Part of the testing process that problems go through, before being used officially, involves being used as experimental questions on real GMATs. When a problem is in this stage, the test writers check to make sure that high scorers are consistently getting that problem right. In a situation like the one you describe - where it's ambiguous what you're supposed to do, and there's no clear way to tell - then some high scorers would get one answer (because they did the right math and decided to ignore the second crossing), and other high scorers would get a different answer (because they did the right math and decided to have the people turn around at the second crossing.) So, the problem would be thrown out or rewritten.

In short: don't worry about this - worry about perfecting your technique and speed on easier rates problems instead.

Aadi01 · Answer

Please provide a link to such an example if have any

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