document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207751>Question 1207751</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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<BR>\n" );
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document.write( "Let me see.\r<BR>\n" );
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document.write( "Patrick = 1/10\r<BR>\n" );
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document.write( "April = 1/x\r<BR>\n" );
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document.write( "Together = 1/6\r<BR>\n" );
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document.write( "(1/10) + (1/x) = (1/6)\r<BR>\n" );
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document.write( "Is this the correct equation?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845832 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=845832\">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 so far.\r<BR>\n" );
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document.write( "I'll show two ways of solving that equation.<BR>\n" );
document.write( "Here is one way.<BR>\n" );
document.write( "1/10 + 1/x = 1/6<BR>\n" );
document.write( "30x(1/10 + 1/x) = 30x(1/6)<BR>\n" );
document.write( "3x + 30 = 5x<BR>\n" );
document.write( "30 = 5x-3x<BR>\n" );
document.write( "30 = 2x<BR>\n" );
document.write( "2x = 30<BR>\n" );
document.write( "x = 30/2<BR>\n" );
document.write( "<font color=red>x = 15 hours</font> is the amount of time April takes when working alone.\r<BR>\n" );
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document.write( "Or you can solve it like this.<BR>\n" );
document.write( "1/10 + 1/x = 1/6<BR>\n" );
document.write( "x/(10x) + 10/(10x) = 1/6<BR>\n" );
document.write( "(x+10)/(10x) = 1/6<BR>\n" );
document.write( "6(x+10) = 10x<BR>\n" );
document.write( "6x+60 = 10x<BR>\n" );
document.write( "60 = 10x-6x<BR>\n" );
document.write( "60 = 4x<BR>\n" );
document.write( "4x = 60<BR>\n" );
document.write( "x = 60/4<BR>\n" );
document.write( "<font color=red>x = 15 hours</font>\r<BR>\n" );
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document.write( "--------------------------------------------------------------------------\r<BR>\n" );
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document.write( "Another approach\r<BR>\n" );
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document.write( "Let's say hypothetically that the total surface area to paint all four rooms is 600 square feet.\r<BR>\n" );
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document.write( "Patrick, when working alone, can paint all 600 square feet in 10 hours.<BR>\n" );
document.write( "His unit rate is 600/10 = 60 sq ft per hour.<BR>\n" );
document.write( "Formula:  rate = amountDone/time\r<BR>\n" );
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document.write( "When Patrick and April work together, they get the job done in 6 hours. <BR>\n" );
document.write( "I'll assume neither person slows down the other.<BR>\n" );
document.write( "Their combined unit rate is 600/6 = 100 sq ft per hour.\r<BR>\n" );
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document.write( "Therefore, April's unit rate must be 100-60 = 40 sq ft per hour when she works alone.\r<BR>\n" );
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document.write( "Let's determine how long April will take when she does the job alone.<BR>\n" );
document.write( "rate*time = amountDone<BR>\n" );
document.write( "time = amountDone/rate<BR>\n" );
document.write( "time = 600/40<BR>\n" );
document.write( "time = <font color=red>15 hours</font>\r<BR>\n" );
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document.write( "The hypothetical 600 sq ft figure I came up with isn't special at all. Turns out you can replace it with any other positive number to get the same final answer marked in red.<BR>\n" );
document.write( "I picked 600 since 10*6 = 60, and then I tacked a zero at the end to make the area appear a a bit more realistic pertaining to those four rooms.<BR>\n" );
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