document.write( "Question 1158064: Cara and Jim, working together, can weed the garden in 2 hours. Working alone, Jim takes twice as long as Cara. How long does it take Cara to weed the garden alone?\r
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Algebra.Com's Answer #780996 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let C be the rate of work by Cara, and let J be the rate of work of Jim.\r\n" );
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document.write( "Then from the condition, you have these two equations\r\n" );
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document.write( "    C + J = \"1%2F2\"    (1)   (their combined rate of work is \"1%2F2\" of the job per hour)\r\n" );
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document.write( "    C = 2J        (2)    (Cara's rate is twice the Jim's rate)\r\n" );
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document.write( "Next. you substitute expression (2) into (1), and you get\r\n" );
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document.write( "    2J + J = \"1%2F2\",   or\r\n" );
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document.write( "    3J = \"1%2F2\",  J = \"1%2F6\".   \r\n" );
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document.write( "It means that Jim will complete the job alone in 6 hours.\r\n" );
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document.write( "It implies that Cara will complete the job in 3 hours, working alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "If this solution seems to be too complicated, there is another way, without using equation.\r
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\n" ); document.write( "\n" ); document.write( "You may interpret the condition in this way:\r
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document.write( "    Two instances of Jim (as Cara) and one real Jim can complete the job in 2 hours.\r\n" );
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document.write( "    2 + 1 = 3.\r\n" );
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document.write( "    Hence, Jim alone can do the job in 2*3 = 6 hours.\r\n" );
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document.write( "    Cara takes only half of that time, i.e. 6:2 = 3 hours.\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is a standard and typical joint work problem.\r
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\n" ); document.write( "\n" ); document.write( "There is a wide variety of similar solved joint-work problems with detailed explanations in this site.  See introductory lessons\r
\n" ); document.write( "\n" ); document.write( "    - Using Fractions to solve word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Solving more complicated word problems on joint work \r
\n" ); document.write( "\n" ); document.write( "    - Selected joint-work word problems from the archive \r
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\n" ); document.write( "\n" ); document.write( "Read them and get be trained in solving joint-work problems.\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-I in this site\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic
\n" ); document.write( "\"Rate of work and joint work problems\"  of the section  \"Word problems\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
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\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
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