document.write( "Question 683812: Two trains of equal length are on parallel tracks. One train is travelling at
\n" ); document.write( "40 km/h and the other at 20 km/h. It takes two minutes longer for the trains
\n" ); document.write( "to completely pass one another when going in the same direction, than when
\n" ); document.write( "going in opposite directions.
\n" ); document.write( "Determine the length of each train. \n" ); document.write( "

Algebra.Com's Answer #423760 by Edwin McCravy(20056) $\"\"$ $\"About$

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Two trains of equal length are on parallel tracks. One train is travelling at
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\n" ); document.write( "to completely pass one another when going in the same direction, than when
\n" ); document.write( "going in opposite directions.
\n" ); document.write( "Determine the length of each train.
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document.write( "Let's convert their speeds to km/minute\r\n" );
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document.write( "20 km/h =  km/minute =  km/minute\r\n" );
document.write( "40 km/h =  km/minute =  km/minute\r\n" );
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document.write( "Let each train's length be x, and the time to pass when going in\r\n" );
document.write( "opposite directions be t minutes.  Then the time to pass when going in\r\n" );
document.write( "the same directions will be t+2.\r\n" );
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document.write( "Here they are going in opposite directions starting to pass each other:\r\n" );
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document.write( "  \r\n" );
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document.write( "Suppose the train on the left is the faster train.  For the train on the \r\n" );
document.write( "left to pass the train on the right, point A must move to be even with \r\n" );
document.write( "point B.  \r\n" );
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document.write( "Point A is approaching point B at a rate equal to the sum of the rates\r\n" );
document.write( "or  or 1 km/minute. Point A's distance to point B is 2x.\r\n" );
document.write( "Since distance = rate·time, we have 2x = 1·t\r\n" );
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document.write( "Here they are going in the same direction, the faster starting to pass\r\n" );
document.write( "the slower.\r\n" );
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document.write( "  \r\n" );
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document.write( "Suppose again the train on the left is the faster train.  As above, for the\r\n" );
document.write( "train on the left to pass the train on the right, point A must move to be \r\n" );
document.write( "even with point B.  In this case Point A is approaching point B at a rate equal\r\n" );
document.write( "to the difference of the rates or  or  km/minute. Again, point A's distance \r\n" );
document.write( "to point B is 2x. Since distance = rate·time, in this case we have 2x = ·(t+2).\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "2x = 1·t\r\n" );
document.write( "2x = ·(t+2)\r\n" );
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document.write( "Solve that system by substitution and get\r\n" );
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document.write( "x = 0.5 km, and t = 1 minute\r\n" );
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document.write( "Each train is 0.5 km long and it takes 1 minute for them to pass \r\n" );
document.write( "each other when going in opposite directions and 1+2 or 3 minutes \r\n" );
document.write( "for the faster to pass the slower when going in the same direction.\r\n" );
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document.write( "Edwin

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