document.write( "Question 446267: Trains a and b are traveling in the same directions on parallel tracks. Train a is traveling at 80 miles per hour and train b is traveling at 90 miles per hour train a passes a station at 9:15 p.m. if train b passes the same station at 9:45 p.m. at what time will train b catch up to train a? \n" ); document.write( "
Algebra.Com's Answer #307315 by Edwin McCravy(20060)\"\" \"About 
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Trains A and B are traveling in the same directions on parallel tracks. Train A is traveling at 80 miles per hour and train B is traveling at 90 miles per hour train A passes a station at 9:15 p.m. if train B passes the same station at 9:45 p.m. at what time will train B catch up to train A?
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document.write( "Two ways to do it: a) in your head or b) by algebra\r\n" );
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document.write( "First way. In your head using the \"catch-up\" rate of 90-80 or 10mph.\r\n" );
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document.write( "In the half hour from 9:15 to 9:45, train A has gone 40 miles from \r\n" );
document.write( "the station. So train B has to catch up that 40 miles between them \r\n" );
document.write( "at a catch-up rate of 10 mph, and so that will take B 4 hours to \r\n" );
document.write( "catch up to A.\r\n" );
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document.write( "Second way: By algebra:\r\n" );
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document.write( "Make this chart. \r\n" );
document.write( "           distance  = rate  × time\r\n" );
document.write( "Teain A    \r\n" );
document.write( "Train B      \r\n" );
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document.write( "Let t = the time it takes B to catch up to A, which is\r\n" );
document.write( "what we want to find.\r\n" );
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document.write( "           distance  = rate  × time\r\n" );
document.write( "Train A     \r\n" );
document.write( "Train B                          t\r\n" );
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document.write( "Sinse A traveled 1/2 an hour longer than B did,\r\n" );
document.write( "we fill in A's time as t+1/2 \r\n" );
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document.write( "Fill in the two rates:\r\n" );
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document.write( "           distance  = rate  × time\r\n" );
document.write( "Train A                 80     t+1/2 \r\n" );
document.write( "Train B                 90      t\r\n" );
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document.write( "Fill in the distances using d=rt\r\n" );
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document.write( "           distance  = rate  × time\r\n" );
document.write( "Teain A    80(t+1/2)    80     t+1/2 \r\n" );
document.write( "Train B      90t        90      t\r\n" );
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document.write( "Those two distances from the station are equal\r\n" );
document.write( "when B catches up to A, so set them equal:\r\n" );
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document.write( "      80(t+1/2) = 90t\r\n" );
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document.write( "Solve that and get 4 hours.\r\n" );
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document.write( "Edwin
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