document.write( "Question 131749: Please help me solve this word problem:\r
\n" ); document.write( "\n" ); document.write( "Chip and Layla found a hole in the fence and decided to make a run for it at the same time. Chip headed north trotting at x miles per hour. Layla ran east, running 2 miles an hour faster than Chip. In 2 hours, they were 20 miles apart (as the crow flies- think hypotenuse). How fast was each dog going? \n" ); document.write( "
Algebra.Com's Answer #96184 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "SOLVER91311'S SOLUTION IS INCORRECT BECAUSE HE
\n" ); document.write( "FORGOT TO INCLUDE THE \"2 HOURS\" IN HIS EQUATION.
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\n" ); document.write( "Correct solution:
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document.write( "Let R = Chip's northward rate in mi/h\r\n" );
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document.write( "Chip's time is 2 hours\r\n" );
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document.write( "Using DISTANCE = RATE x TIME,\r\n" );
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document.write( "Distance of Chip's northward path = (R)(2) = 2R mi\r\n" );
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document.write( ">>...Layla ran east, running 2 miles an hour faster than Chip...<<\r\n" );
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document.write( "Therefore Layla's eastward rate is R+2\r\n" );
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document.write( "Using DISTANCE = RATE x TIME,\r\n" );
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document.write( "Distance of Layla's eastward path = (R+2)2 = 2(R+2) = 2R+4 mi.\r\n" );
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document.write( "We'll write those distances on the appropriate sides of the \r\n" );
document.write( "triangle.\r\n" );
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document.write( "So we use the Pythagorean theorem:\r\n" );
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document.write( "                   a² + b² = c²\r\n" );
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document.write( "           (2R)² + (2R+4)² = 20²\r\n" );
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document.write( "        4R² + (2R+4)(2R+4) = 400\r\n" );
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document.write( "4R² + (4R² + 8R + 8R + 16) = 400\r\n" );
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document.write( "    4R² + (4R² + 16R + 16) = 400\r\n" );
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document.write( "      4R² + 4R² + 16R + 16 = 400\r\n" );
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document.write( "            8R² + 16R + 16 = 400\r\n" );
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document.write( "           8R² + 16R - 384 = 0\r\n" );
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document.write( "Divide every term thru by 8\r\n" );
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document.write( "              R² + 2R - 48 = 0\r\n" );
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document.write( "            (R - 6)(R + 8) = 0\r\n" );
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document.write( "Solutions are R = 6 and R = -8\r\n" );
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document.write( "We discard the negative solution.\r\n" );
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document.write( "Solution:  Chip's rate = R = 6 mi/h\r\n" );
document.write( "           Layla's rate = R+2 = 6+2 = 8 mi/h\r\n" );
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document.write( "Edwin
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