document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208959>Question 1208959</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Patrice, 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<BR>\n" );
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document.write( "Let A = length of time it will take April to paint four rooms\r<BR>\n" );
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document.write( "Here is my equation:\r<BR>\n" );
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document.write( "(1/10) + (1/A) = 1/6\r<BR>\n" );
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document.write( "Is this correct? \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847505 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=847505\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "You have the correct set up. <BR>\n" );
document.write( "To solve you can multiply everything by the LCD 30A and you should get 3A+30 = 5A. <BR>\n" );
document.write( "Which at this point should be fairly easy to solve.<BR>\n" );
document.write( "The result is <font color=red>A = 15</font>.\r<BR>\n" );
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document.write( "Another option is to solve like so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10%2B1%2FA+=+1%2F6 ALIGN=MIDDLE  ALT=\"1%2F10%2B1%2FA+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2F%2810A%29%2B10%2F%2810A%29+=+1%2F6 ALIGN=MIDDLE  ALT=\"A%2F%2810A%29%2B10%2F%2810A%29+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite each fraction in terms of a common denominator\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28A%2B10%29%2F%2810A%29+=+1%2F6 ALIGN=MIDDLE  ALT=\"%28A%2B10%29%2F%2810A%29+=+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%28A%2B10%29+=+10A ALIGN=MIDDLE  ALT=\"6%28A%2B10%29+=+10A\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cross multiply\r<BR>\n" );
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document.write( "I'll let the student take over from here. \r<BR>\n" );
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document.write( "Another approach.\r<BR>\n" );
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document.write( "Let's say the job is to paint 600 square feet of wall and ceiling area. <BR>\n" );
document.write( "I arrived at this number by multiplying the given values 10 and 6. <BR>\n" );
document.write( "Then tacking on a 0 at the end to make the area a bit more realistic.\r<BR>\n" );
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document.write( "This number isn't particularly important since it can be changed to anything else. You will get the same result at the end.<BR>\n" );
document.write( "Also, the \"four rooms\" can be changed to any number of rooms to get the same answer. So we'll ignore this figure.\r<BR>\n" );
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document.write( "Patrice can paint all 600 sq ft in 10 hours when working alone.<BR>\n" );
document.write( "His rate is 600/10 = 60 sq ft per hour.<BR>\n" );
document.write( "rate = amountDone/time\r<BR>\n" );
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document.write( "When Patrice and April work together, assuming neither person hinders the other, they paint all 600 sq ft in 6 hours.<BR>\n" );
document.write( "rate = 600/6 = 100 sq ft per hour.\r<BR>\n" );
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document.write( "April's unit rate must be 100-60 = 40 sq ft per hour since the two people's individual rates add to the combined rate 100 sq ft per hour.\r<BR>\n" );
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document.write( "Let's see how long it takes her to do the job by herself.<BR>\n" );
document.write( "rate*time = amountDone<BR>\n" );
document.write( "time = amountDone/rate<BR>\n" );
document.write( "time = (600 sq ft)/(40 sq ft per hr)<BR>\n" );
document.write( "time = (600/40) hours<BR>\n" );
document.write( "time = <font color=red>15 hours</font><BR>\n" );
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