document.write( "Question 1208315: Two trains are approaching each other on parallel tracks. Train A is 1/5 of a mile in length. It travels east at a speed of 40 mph. Train B is 1/8 of a mile in length. It travels west at a speed of 50 mph.\r
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Algebra.Com's Answer #846657 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Think of the two parallel tracks as identical number lines.\r\n" );
document.write( "Suppose the longer train is traveling to the right (east) and the shorter train\r\n" );
document.write( "is traveling to the left (west).\r\n" );
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document.write( "The speed of the longer train headed right will be taken as a POSITIVE speed \r\n" );
document.write( "and the speed of the shorter train headed left will be taken as a NEGATIVE\r\n" );
document.write( "speed. \r\n" );
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document.write( "The noses of the trains are side by side at time t=0 and their noses are both\r\n" );
document.write( "at point 0 on their number lines (their tracks).\r\n" );
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document.write( "The tail of the long train is at point -1/5 at time t=0.\r\n" );
document.write( "The tail of the short train is at point +1/8 at time t=0.\r\n" );
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document.write( "We want to know when the tails of the trains will be side-by-side at the same\r\n" );
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document.write( "The longer train's tail is at point -1/5 at time t=0 and is traveling at rate\r\n" );
document.write( "+40 mph.\r\n" );
document.write( "The shorter train's tail is at +1/8 at time t=0 and is traveling at rate \r\n" );
document.write( "-50 mph.\r\n" );
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document.write( "Using DISTANCE = RATE x TIME:\r\n" );
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document.write( "At time t, the longer train's nose is at point 40t and so its tail is 1/5 mile\r\n" );
document.write( "further to the left, that is, at 40t-1/5\r\n" );
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document.write( "At time t, the shorter train's nose is at point -50t and so its tail is \r\n" );
document.write( "1/8 mile further to the right, that is, at -50t+1/8\r\n" );
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document.write( "Remember, we want to know when the tails of the trains will be side by side at\r\n" );
document.write( "the same point on the number lines.\r\n" );
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document.write( "We set them equal and get \r\n" );
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document.write( " of an hour.\r\n" );
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document.write( "That is a very convenient denominator, for\r\n" );
document.write( "since there are 60x60=3600 seconds in an hour,\r\n" );
document.write( "that means the answer is 13 seconds.\r\n" );
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document.write( "[In case you're interested in where on the number line (track) that will\r\n" );
document.write( "occur, it will be at -293 1/3 feet. That means they will have passed each\r\n" );
document.write( "other 293 1/3 feet before the longer train's tail has reached the point 0 \r\n" );
document.write( "on the tracks, and where the shorter train is 293 1/3 feet left of\r\n" );
document.write( "the point 0, (where their noses were side by side).]\r\n" );
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document.write( "Edwin

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