document.write( "Question 1207751: Patrick, by himself, can paint four rooms in 10 hours. If he hires April to help, they can do the same job together in 6 hours. If he lets April work alone, how long will it take her to paint four rooms?\r
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\n" ); document.write( "\n" ); document.write( "Let me see.\r
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\n" ); document.write( "\n" ); document.write( "Patrick = 1/10\r
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\n" ); document.write( "\n" ); document.write( "April = 1/x\r
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\n" ); document.write( "\n" ); document.write( "Together = 1/6\r
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\n" ); document.write( "\n" ); document.write( "(1/10) + (1/x) = (1/6)\r
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\n" ); document.write( "\n" ); document.write( "Is this the correct equation? \n" ); document.write( "

Algebra.Com's Answer #845803 by ikleyn(52754) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "        Yes, this setup equation is correct.\r
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\n" ); document.write( "\n" ); document.write( "        You can continue and solve it.\r
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\n" ); document.write( "\n" ); document.write( "        But this problem can be solved without using any equation,
\n" ); document.write( "        by manipulating fractions, ONLY.\r
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\n" ); document.write( "\n" ); document.write( "        See the reasoning below.\r
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document.write( "Patrick and April can do the job together in 6 hours.\r\n" );
document.write( "Hence, their combined rate of work is    of the job per hour.\r\n" );
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document.write( "Patrick, working alone, can do the job in 10 hours.\r\n" );
document.write( "Hence, Patrick's rate of work is    of the job per hour.\r\n" );
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document.write( "Hence, April's rate of work is the difference\r\n" );
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document.write( "     -  =  =  =  = .\r\n" );
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document.write( "It means that April makes 1/15 of the job per hour.\r\n" );
document.write( "Hence, April needs 15 hours to complete the job working alone.\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved in full, with complete explanations.\r
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\n" ); document.write( "\n" ); document.write( "So, you can solve this problem in two ways :   manipulating with fractions or using equations.\r
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\n" ); document.write( "\n" ); document.write( "Both methods have equal rights to exist.\r
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\n" ); document.write( "\n" ); document.write( "Both methods implement the same idea: making a balance of rates of work.\r
\n" ); document.write( "\n" ); document.write( "One method implements it using manipulations with fractions;\r
\n" ); document.write( "\n" ); document.write( "other method implements it using equations.\r
\n" ); document.write( "\n" ); document.write( "But the idea of the solution is the same in both methods - only the implementation forms are different.\r
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\n" ); document.write( "\n" ); document.write( "Solving by manipulating fractions is accessible method for 5-th or 6-th grade students.\r
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\n" ); document.write( "\n" ); document.write( "Solving using equations is accessible method for 7-th grade students, who are just familiar with equations.\r
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\n" ); document.write( "\n" ); document.write( "To see many other similar (and different) problems on joint work,
\n" ); document.write( "solved with complete explanations to teach you, look into the lessons\r
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\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( "Consider these lessons as your textbook, handbook, guidebook, tutorials and (free of charge) home teacher,
\n" ); document.write( "which is always with you to help and to inspire.\r
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\n" ); document.write( "\n" ); document.write( "By the way, this problem was solved at this forum many years ago (perhaps, 20 years ago).
\n" ); document.write( "For the solutions, see the links\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Rate-of-work-word-problems.faq.question.264833.html\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.68586.html#google_vignette\r
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