document.write( "Question 1151457: The average speed of an airplane is four times as fast as the average speed of a passenger train. To travel 1440 km, the train requires 12h more than the airplane. Determine the average speeds of the train and the airplane.
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Algebra.Com's Answer #773210 by ikleyn(52814) $\"\"$ $\"About$

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document.write( "Let r be the average speed of the train, in kilometers per hour;\r\n" );
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document.write( "Then the average speed of the train is 4r,  according to the condition.\r\n" );
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document.write( "Time to travel 1440 km by train is    hours.\r\n" );
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document.write( "Time to travel 1440 km by airplane is    hours.\r\n" );
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document.write( "The difference of times is 12 hours.  It gives you this \"time\" equation\r\n" );
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document.write( "     -  = 12  hours.     (1)\r\n" );
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document.write( "The second fraction in the left side is  , so this equation takes the form\r\n" );
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document.write( "     -  = 12,   or\r\n" );
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document.write( "     = 12.\r\n" );
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document.write( "Then  r =  = 90.\r\n" );
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document.write( "ANSWER.  The average speed of the train is 90 km/h.\r\n" );
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document.write( "         The average speed of the airplane is 4 times 90 km/h,  or  360 km/h.\r\n" );
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document.write( "CHECK.  I will check equation (1).\r\n" );
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document.write( "         -  = 16 - 4 = 12 hours.   ! Precisely correct !\r\n" );
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