document.write( "Question 483613: Please help me to solve : Jack usually mows the lawn in 3 hours. Marilyn can mow the same yard in 6 hours. How much time would it take for them to mow the lawn together? \n" ); document.write( "

Algebra.Com's Answer #330928 by Edwin McCravy(20060) $\"\"$ $\"About$

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Please help me to solve : Jack usually mows the lawn in 3 hours. Marilyn can
\n" ); document.write( "mow the same yard in 6 hours. How much time would it take for them to mow the
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document.write( "Make this chart:                 |  Number of   |         | rate in\r\n" );
document.write( "                                 | lawns mowed  |  hours  | lawns/hr.\r\n" );
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document.write( "Jack working alone               |              |         | \r\n" );
document.write( "Marilyn working alone            |              |         |\r\n" );
document.write( "Jack and Marilyn working together|              |         |\r\n" );
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document.write( "We want to know the number of hours it will take Jack and Marilyn if they work\r\n" );
document.write( "together.  Let that be x hours to mow 1 lawn so we fill in x for the hours they\r\n" );
document.write( "will take and 1 for the number of laws they will mow working together. \r\n" );
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document.write( "                                 |  Number of   |  no. of | rate in\r\n" );
document.write( "                                 | lawns mowed  |  hours  | lawns/hr.\r\n" );
document.write( "---------------------------------------------------------------------\r\n" );
document.write( "Jack working alone               |              |         | \r\n" );
document.write( "Marilyn working alone            |              |         |\r\n" );
document.write( "Jack and Marilyn working together|      1       |    x    |\r\n" );
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document.write( "Jack mows 1 lawn in 3 hours, so we fill in 1 for the number of lawns\r\n" );
document.write( "he mows and 3 for the number of hours it takes him:\r\n" );
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document.write( "Similarly, Marilyn mows 1 lawn in 6 hours, so we fill in 1 for the \r\n" );
document.write( "number of lawns she mows and 6 for the number of hours it takes her:\r\n" );
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document.write( "                                 |  Number of   |  no. of | rate in\r\n" );
document.write( "                                 | lawns mowed  |  hours  | lawns/hr.\r\n" );
document.write( "---------------------------------------------------------------------\r\n" );
document.write( "Jack working alone               |      1       |    3    |   \r\n" );
document.write( "Marilyn working alone            |      1       |    6    |   \r\n" );
document.write( "Jack and Marilyn working together|      1       |    x    |   \r\n" );
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document.write( "Next we find the rates in lawns/hr by dividing lawns mowed by hours:\r\n" );
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document.write( "                                 |  Number of   |  no. of | rate in\r\n" );
document.write( "                                 | lawns mowed  |  hours  | lawns/hr.\r\n" );
document.write( "---------------------------------------------------------------------\r\n" );
document.write( "Jack working alone               |      1       |    3    |   1/3\r\n" );
document.write( "Marilyn working alone            |      1       |    6    |   1/6 \r\n" );
document.write( "Jack and Marilyn working together|      1       |    x    |   1/x\r\n" );
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document.write( "   The equation comes from:\r\n" );
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document.write( "          Jack's rate + Marilyn's rate = their combined rate\r\n" );
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document.write( "                             1/3 + 1/6 = 1/x\r\n" );
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document.write( "Multiply through by the LCD which is 6x\r\n" );
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document.write( "                                2x + x = 6\r\n" );
document.write( "                                    3x = 6\r\n" );
document.write( "                                     x = 2\r\n" );
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document.write( "So it would take them 2 hours working together.   \r\n" );
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document.write( "Edwin

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