document.write( "Question 37145: HELP!!! I have worked this problem and can't get it.\r
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\n" ); document.write( "\n" ); document.write( "Jim can run 5 miles per hour on level ground on a still day. One windy day, he runs 10 miles with the wind, and in the same amount of time runs 4 miles against the wind. What is the rate of the wind? \n" ); document.write( "
Algebra.Com's Answer #22830 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Problem: \r\n" );
document.write( "Jim can run 5 miles per hour on level ground on a still day. \r\n" );
document.write( "One windy day, he runs 10 miles with the wind, and in the same \r\n" );
document.write( "amount of time runs 4 miles against the wind. What is the rate \r\n" );
document.write( "of the wind?\r\n" );
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document.write( "Make this chart\r\n" );
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document.write( "               DISTANCE      RATE       TIME\r\n" );
document.write( "With wind                                      \r\n" );
document.write( "Against wind \r\n" );
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document.write( ">>...he runs 10 miles with the wind, and in the same amount of time \r\n" );
document.write( "runs 4 miles against the wind...<<\r\n" );
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document.write( "Fill in the two distances                                  \r\n" );
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document.write( "               DISTANCE      RATE       TIME\r\n" );
document.write( "With wind         10                            \r\n" );
document.write( "Against wind       4                           \r\n" );
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document.write( "Let the rate of the wind be x miles per hour. \r\n" );
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document.write( "So when running with the wind, his rate is increased by x mph.\r\n" );
document.write( "So we add x to his rate of 5mph and get 5+x mph, so fill that\r\n" );
document.write( "rate in: \r\n" );
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document.write( "               DISTANCE      RATE       TIME\r\n" );
document.write( "With wind         10         5+x      \r\n" );
document.write( "Against wind       4        \r\n" );
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document.write( "When running against the wind, his rate is decreased by x mph.\r\n" );
document.write( "So we subtract x from his rate of 5mph and get 5-x mph, so fill \r\n" );
document.write( "that rate in: \r\n" );
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document.write( "               DISTANCE      RATE       TIME\r\n" );
document.write( "With wind         10         5+x      \r\n" );
document.write( "Against wind       4         5-x\r\n" );
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document.write( "Now use TIME = DISTANCE/RATE to fill in the two times:\r\n" );
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document.write( "               DISTANCE      RATE       TIME\r\n" );
document.write( "With wind         10         5+x      10/(5+x)\r\n" );
document.write( "Against wind       4         5-x       4/(5-x)\r\n" );
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document.write( ">>>...in the same amount of time...<<\r\n" );
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document.write( "This says the two times are equal:\r\n" );
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document.write( "               10      4\r\n" );
document.write( "             ————— = —————\r\n" );
document.write( "              5+x     5-x  \r\n" );
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document.write( "Multiply thru by LCD = (5+x)(5-x)\r\n" );
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document.write( "           10(5-x) = 4(5+x)\r\n" );
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document.write( "          50 - 10x = 20 + 4x\r\n" );
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document.write( "              -14x = -30\r\n" );
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document.write( "                 x = (-30)/(-14)\r\n" );
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document.write( "                 x = 15/7 or 2 1/7 mph\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "When he runs with the wind he runs 5 + 2 1/7 mph or 7 1/7 mph \r\n" );
document.write( "or 50/7 mph for 10 miles.  Since T = D/R, his time is 10/(50/7)\r\n" );
document.write( "= 7/5 hours\r\n" );
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document.write( "When he runs against the wind he runs 5 - 2 1/7 mph or 2 6/7 mph\r\n" );
document.write( "or 20/7 mph for 4 miles.  Since T = D/R, his time is 4/(20/7)\r\n" );
document.write( "= 7/5 hours\r\n" );
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document.write( "So the times are equal, thus the answer is correct.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com

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