document.write( "Question 282326: Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks. If his total time is 75 minutes, then what is Amit's running speed? \n" ); document.write( "

Algebra.Com's Answer #854184 by ikleyn(53742) $\"\"$ $\"About$

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\n" ); document.write( "Each day, Amit runs nine miles and then walks one mile. He runs 10 mph faster than he walks.
\n" ); document.write( "If his total time is 75 minutes, then what is Amit's running speed?
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\n" ); document.write( "\n" ); document.write( " The solution and the answer in the post by @mananth both are incorrect due to arithmetic errors on the way.\r
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document.write( "let him walk at x mph\r\n" );
document.write( "he runs x+10 mph\r\n" );
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document.write( "time taken for running = 9/x+10\r\n" );
document.write( "time he walks = 1/x\r\n" );
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document.write( "Time equation\r\n" );
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document.write( "    1/x + 9/(x+10) = 5/4 hours\r\n" );
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document.write( "Simplify and find x\r\n" );
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document.write( "    4(x+10) + 36x = 5x(x+10)\r\n" );
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document.write( "    4x + 40 + 36x = 5x^2 + 50x\r\n" );
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document.write( "    40x + 40 = 5x^2 + 50x\r\n" );
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document.write( "    5x^2 + 10x - 40 = 0\r\n" );
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document.write( "    x^2 + 2x - 8 = 0\r\n" );
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document.write( "    (x+4)*(x-2) = 0.\r\n" );
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document.write( "The roots are x= -4 and x= 2.\r\n" );
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document.write( "Since we look for the speed, we accept the positive root x= 2 and reject the negative one.\r\n" );
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document.write( "ANSWER.  Amit's walking speed is 2 miles per hour and his running speed is 2+10 = 12 mph.\r\n" );
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document.write( "CHECK for the travel time.   =  =  =  of an hour.\r\n" );
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document.write( "                            ! precisely correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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