document.write( "Question 1150457: Chris and Pat exercise together by running opposite directions around a 108m circular track for 45 minutes. Starting together, Chris’ velocity is 5 2/3 meters per second while Pat runs 3 1/3 m/s. How many times do they pass one another in 45 minutes? \n" ); document.write( "

Algebra.Com's Answer #771827 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "For the first time, they will meet each other, when the sum of the distances they cover will be exactly the length of the track\r\n" );
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document.write( "    . + . = 108  meters,   or\r\n" );
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document.write( "    ( + ). = 108\r\n" );
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document.write( "    9t = 108\r\n" );
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document.write( "     t =  = 12 seconds.\r\n" );
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document.write( "So, for the first time they will meet each other in 12 seconds.\r\n" );
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document.write( "After that, they are in the same situation, as originally: they start from the common point and move \r\n" );
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document.write( "in opposite directions, with the same rates as before.  Hence, they meet each other again in 12 seconds next time.\r\n" );
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document.write( "Now it should be clear to you that they will meet each other EVERY 12 seconds.\r\n" );
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document.write( "So, to get the answer, you should divide 45 minutes by 12 seconds -- in this way you will get \r\n" );
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document.write( "    45 minutes divided by 12 seconds = 45 minutes divided by  of the minute = 45*5 = 225 times.\r\n" );
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document.write( "ANSWER.  225 times. \r\n" );
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document.write( "         We do not count the starting point.\r\n" );
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document.write( "         We count their last meeting at the end of the 45-th minute.\r\n" );
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