Question 1088379
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A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hours respectively. 
If they start at 8 AM from the same point in opposite directions, how many times shall they cross each other before 9 30 AM ?
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1.  Let answer first more simple question:


        if they start from the same point in opposite directions at 8 am, when they meet each other next time ?


    It is clear that they will meet each other next time when <U>the sum of distances</U> covered by each along the circumference 
    becomes EXACTLY equal to one circle  length.

    Next, the rate of A is 2 rounds per hour; the rate of B is 3 rounds per hour;

    HENCE, their relative speed is (2+3) = 5 rounds per hour.


    So, they meet each other next time in 12 minutes = {{{1_hour/5_rounds}}}, 
        at 8:12 am.


2.  From his point, it is clear that they will meet each other EVERY 12 minutes.


    Now, how much room there is in 90 minutes for 12 minute intervals ?


    It is easy question: {{{90/12}}} = 7.5 times.


3.  So, if you start count from 8:00 when A and B are close to each other for the first time, you will count 7 times more when they meet each other.
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Hope I answered your question.



Similar problems are considered at the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/travel/Problems-on-bodies-moving-on-a-circle.lesson>Problems on bodies moving on a circle</A>

in this site.



Also, you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this textbook under the section "<U>Word problems</U>", the topic "<U>Travel and Distance problems</U>".