document.write( "Question 1073420: Rates of Two Trains\r
\n" ); document.write( "\n" ); document.write( "a)Solve using on variable. Two trains depart simultaneously from a station, traveling in opposite directions. One average 80 km/h and the other 100 km/h. Determine how long it will take the trains to be 450 km apart.\r
\n" ); document.write( "\n" ); document.write( "b)Solve using two variables. Two trains depart simultaneously from a station, traveling in opposite directions. One average 8 km/h more than the other, and after 1/2 hour they are 100 km apart. Determine the speed of each train. \n" ); document.write( "

Algebra.Com's Answer #688257 by ikleyn(52812) $\"\"$ $\"About$

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\n" ); document.write( "a) Solve using on variable. Two trains depart simultaneously from a station, traveling in opposite directions.
\n" ); document.write( "One average 80 km/h and the other 100 km/h. Determine how long it will take the trains to be 450 km apart.\r
\n" ); document.write( "\n" ); document.write( "b) Solve using two variables. Two trains depart simultaneously from a station, traveling in opposite directions.
\n" ); document.write( "One average 8 km/h more than the other, and after 1/2 hour they are 100 km apart. Determine the speed of each train.
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document.write( "a) Let t be the time under the question.\r\n" );
document.write( "   Then  the distance traveled by the first  train is  80*t kilometers,\r\n" );
document.write( "   while the distance traveled by the second train is 100*t kilometers.\r\n" );
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document.write( "   The equation is \r\n" );
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document.write( "       80t + 100t = 450,  or\r\n" );
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document.write( "       180t = 450,  which gives  t =  =  = 2.5 hours = 2 hours and 30 minutes.\r\n" );
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document.write( "Answer.  2.5 hours = 2 hours and 30 minutes.\r\n" );
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document.write( "b) Let x be the speed of the first train and y be the speed of the second train.\r\n" );
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document.write( "   Then you have these equations:\r\n" );
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document.write( "       x    -    y =   8,   (1)\r\n" );
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document.write( "       0.5x + 0.5y = 100.    (2)\r\n" );
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document.write( "    From (2), express x = y + 8, and substitute it into (2). You will get\r\n" );
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document.write( "      0.5(y+8) + 0.5y = 100,   or\r\n" );
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document.write( "      0.5y + 4 + 0.5y = 100,\r\n" );
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document.write( "      y = 100 - 4  --->  y = 96.\r\n" );
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document.write( "Answer.  The speed of the second train is 96 km/h;  of the first train 96 + 8 = 104 km/h.\r\n" );
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