document.write( "Question 1162900: Edward takes 15 minutes longer than Kate does to make the 112-mile drive between two cities. Kate drives 8 miles an hour faster. How fast do Edward and Kate drive? \n" ); document.write( "

Algebra.Com's Answer #786802 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let x be the Edward's rate driving, in miles per hour.\r\n" );
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document.write( "Then the Kate's rate driving is  (x+8) mph.\r\n" );
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document.write( "Write the \"time\" equation\r\n" );
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document.write( "     -  =    of an hour.\r\n" );
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document.write( "To solve it, multiply both sides by 4x*(x+8).  You will get\r\n" );
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document.write( "    112*4*(x+8) - 112*4*x = x*(x+8)\r\n" );
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document.write( "    112*4(x+8) - 112*4x = x*(x+8)\r\n" );
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document.write( "    3584 = x*(x+8)      (*)\r\n" );
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document.write( "From this point, there are two ways to complete the solution.\r\n" );
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document.write( "First way is to solve this quadratic equation formally.\r\n" );
document.write( "In this way, you will get the ANSWER 56 mph for Edwards and 64 mph for Kate.\r\n" );
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document.write( "The other way is to introduce new variable y = x+4.\r\n" );
document.write( "Then x+8 = y-4,  and your equation (*)  takes the form\r\n" );
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document.write( "    3584 = (y-4)*(y+4)\r\n" );
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document.write( "    3584 = y^2 - 16\r\n" );
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document.write( "    3584 + 16 = y^2  \r\n" );
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document.write( "    3600 = y^2\r\n" );
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document.write( "    y  =  60\r\n" );
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document.write( "and you get the same answer practically MENTALLY.\r\n" );
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