document.write( "Question 1055380: Jack and Jill can mow the park together in 10 hours. Jack and Joe can mow the same park together in 15 hours. jill and Joe can mow the same park together in 18 hours. Determine the number of hours it would take jill alone to mow the park. Express your answer as a common fraction reduced to lowest terms. \n" ); document.write( "

Algebra.Com's Answer #670626 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Jack and Jill can mow the park together in 10 hours.
\n" ); document.write( "Jack and Joe can mow the same park together in 15 hours.
\n" ); document.write( "Jill and Joe can mow the same park together in 18 hours.
\n" ); document.write( "Determine the number of hours it would take Jill alone to mow the park.
\n" ); document.write( "Express your answer as a common fraction reduced to lowest terms.
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\n" ); document.write( "\n" ); document.write( "There is more short and elegant method to solve this problem.\r
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document.write( "Let \"a\", \"b\" and \"c\" be the rate-of-work of each of the persons Jack, Jill, and Joe, respectively.\r\n" );
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document.write( "We are given that \r\n" );
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document.write( "a + b = ,    (1)\r\n" );
document.write( "a + c = ,    (2)\r\n" );
document.write( "b + c = .    (3)\r\n" );
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document.write( "To solve the system (1), (2), (3), let us start adding the equations (1), (2) and (3). You will get \r\n" );
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document.write( "2a + 2b + 2c =  =  =  =  = .\r\n" );
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document.write( "Hence, \r\n" );
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document.write( "a + b + c = .\r\n" );
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document.write( "Thus we just found the combined rate-of-work of the three persons working together. It is  job per hour.\r\n" );
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document.write( "Now, whose productivity we must to estimate? Jill's alone?\r\n" );
document.write( "Distract the equation (2) from (4). You will get\r\n" );
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document.write( "b =  =  =  = .\r\n" );
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document.write( "It means that Jill alone can mow  of the area per hour.\r\n" );
document.write( "Hence, it will take   = 22.5 hours for Jill to mow the park working alone.\r\n" );
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document.write( "Answer.  It will take  22.5 hours for Jill to mow the park working alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "See also the lesson \r
\n" ); document.write( "\n" ); document.write( " - Joint-work problems for 3 participants, Problem 2\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Very similar problem was solved there using the same method.\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
\n" ); document.write( "\n" ); document.write( " - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this textbook under the topic \"Rate of work and joint work problems\" of the section \"Word problems\".\r
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