Algebra.Com's Answer #657436 by ikleyn(52855)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "Two trains are 500 miles apart when they first start moving towards each other. If in two hours the distance between them
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document.write( "is 300 miles and one train goes 20 miles faster than another, find the speed of the faster train.
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document.write( "(Note: there are two possible solutions. Find both.)
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document.write( "Let \"u\" be the speed of the first (faster) train and \"v\" be the speed of the second train (in miles per hour).\r\n" );
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document.write( "The first equation is \r\n" );
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document.write( "u + v =  ( the distance between the train is decreased at the rate u + v, since they are moving toward each other ).\r\n" );
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document.write( "The second equation is \r\n" );
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document.write( "u - v = 20.\r\n" );
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document.write( "Write both equations as a system:\r\n" );
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document.write( "u + v = 100, (1)\r\n" );
document.write( "u - v = 20. (2)\r\n" );
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document.write( "To solve the system, add equations (1) and (2) (both sides). You will get\r\n" );
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document.write( "2u = 120. Hence, u =  = 60 mph.\r\n" );
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document.write( "Thus the first train speed is 60 mph.\r\n" );
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document.write( "Then the second train speed is v = 100 - v = 40 mph.\r\n" );
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document.write( "Answer. 60 mph and 40 mph.\r\n" );
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