document.write( "Question 197234: Two trains travel at right angles to each other after leaving the same train station at the same time. One hour later they are 100 miles apart. If one travels 20 miles per hour faster than the other, what is the rate of the faster train? I worked it to be 80 mph? \n" ); document.write( "
Algebra.Com's Answer #147861 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let \"d%5B1%5D\" = the distance the slower train had gone after 1 hour.\r\n" );
document.write( "Let \"d%5B2%5D\" = the distance the faster train had gone after 1 hour.\r\n" );
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document.write( "Then by the Pythagorean theorem\r\n" );
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document.write( "\"%28d%5B1%5D%29%5E2+%2B+%28d%5B2%5D%29%5E2+=+%28100%29%5E2\"\r\n" );
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document.write( "Let the rate of the slower train be r.\r\n" );
document.write( "Then the rate of the faster train is r+20. \r\n" );
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document.write( "Using \"distance+=+%28rate%29%28time%29\"\r\n" );
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document.write( "\"d%5B1%5D+=+r%2A1+=+r\"\r\n" );
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document.write( "\"d%5B2%5D+=+%28r%2B20%29%2A1+=+r%2B20\"\r\n" );
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document.write( "So\r\n" );
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document.write( "\"%28d%5B1%5D%29%5E2+%2B+%28d%5B2%5D%29%5E2+=+%28100%29%5E2\"\r\n" );
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document.write( "becomes:\r\n" );
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document.write( "\"%28r%2B20%29%5E2+%2Br%5E2=+10000\"\r\n" );
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document.write( "\"r%5E2%2B40r%2B400%2Br%5E2=10000\"\r\n" );
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document.write( "\"2r%5E2%2B40r-9600=0\"\r\n" );
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document.write( "Divide thru by 2\r\n" );
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document.write( "\"r%5E2%2B20r-4800=0\"\r\n" );
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document.write( "Factoring:\r\n" );
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document.write( "\"%28r-60%29%28r%2B80%29=0\"\r\n" );
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document.write( "\"r-60=0\"\r\n" );
document.write( "\"r=60\"\r\n" );
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document.write( "\"r%2B80=0\"\r\n" );
document.write( "\"r=-80\"\r\n" );
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document.write( "We ignore the negative rate.\r\n" );
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document.write( "So the rate of the slower train is r = 60 mi/h\r\n" );
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document.write( "Therefore the rate of the faster train is r+20 = 60+20 = 80 mi/h\r\n" );
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document.write( "So you were right!  The answer is 80 mi/hr\r\n" );
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document.write( "Edwin
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