document.write( "Question 930764: A and B start together from the same point on a circular track and walk in the same direction till they both again arrive together at the starting point. A completes one circle in 224 s and B in 364 s. How many times will A have passed B?
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Algebra.Com's Answer #565276 by KMST(5328) $\"\"$ $\"About$

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For A and B to arrive together at the starting point,
\n" ); document.write( "each of them must have completed an integer number of turns.
\n" ); document.write( "The time (in seconds) required for that must be a multiple of $\"224\"$ and of $\"364\"$ .
\n" ); document.write( " $\"224=2%5E5%2A7\"$ and $\"364=2%5E2%2A7%2A13\"$ , so
\n" ); document.write( "the minimum common multiple of $\"224\"$ and $\"364\"$ is
\n" ); document.write( " $\"2912=2%5E5%2A7%2A13\"$ .
\n" ); document.write( "That means that A and B first arrive together at the starting point $\"2912\"$ seconds after the start.
\n" ); document.write( "During that time, A will have run $\"2912%2F224=13\"$ laps,
\n" ); document.write( "and $\"B\"$ will have run $\"2912%2F364=8\"$ laps.
\n" ); document.write( "Each time the distance A has run exceeds the distance B has run by an integer (1, 2, 3, or 4 laps), A is passing B.
\n" ); document.write( "When both have run for $\"2912seconds\"$ , A has run $\"13-8=5\"$ more laps than B, and they are both arriving together at the starting point.
\n" ); document.write( "I do not count that time as A passing B,
\n" ); document.write( "because they both stop running at that point,
\n" ); document.write( "so A passes B $\"highlight%284times%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "A MORE DYNAMIC VIEW (in case you do not visualize it yet):
\n" ); document.write( "During their run, A is running at a speed of $\"1%2F224\"$ $\"tracks%2Fsecond\"$ ,
\n" ); document.write( "while B is running at a speed of $\"1%2F364\"$ $\"tracks%2Fsecond\"$ .
\n" ); document.write( "The difference in the distance they have both covered increases at a rate of
\n" ); document.write( " $\"1%2F224-1%2F364=13%2F2912-8%2F2912=5%2F2912\"$ $\"tracks%2Fsecond\"$ ,
\n" ); document.write( "which means $\"5tracks%2F%222912+seconds%22\"$ .
\n" ); document.write( "A will be passing B for the first time when he has run $\"1track\"$ more than B,
\n" ); document.write( "which will take $\"%281track%29%2A%282912seconds%2F%225+tracks%22%29=2912%2F5\"$ $\"seconds=582.4seconds\"$ .
\n" ); document.write( "When they meet at the starting point, after $\"2912seconds\"$ , A will have run
\n" ); document.write( " $\"%282912seconds%29%2A%285tracks%2F%222912+seconds%22%29=5tracks\"$ more than B,
\n" ); document.write( "meaning that A will pass B $\"highlight%284times%29\"$ during the $\"2912seconds\"$ they both run before meeting again
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