document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469791>Question 469791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together? <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 #322292 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=322292\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since Sally can paint a house in 4 hours, in an hour she completes 1/4 of the house.  And since John can paint the same house in 6 hours, in an hour he completes 1/6 of the house.  Therefore, in one hour the sum of their combined efforts is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4+%2B+1%2F6 ALIGN=MIDDLE  ALT=\"1%2F4+%2B+1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "of the job.<BR>\n" );
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document.write( "Add these two fractions by converting them to the common denominator of 12 to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F12+%2B+2%2F12+=+5%2F12 ALIGN=MIDDLE  ALT=\"3%2F12+%2B+2%2F12+=+5%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So in each hour they complete five twelfths of the one job.<BR>\n" );
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document.write( "The question, therefore, is how many hours (call them t for time) does it take for them to complete the entire one job (that is 12 twelfths of the job). Set up the following equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F12%29%2At+=+12%2F12 ALIGN=MIDDLE  ALT=\"%285%2F12%29%2At+=+12%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this equation by first multiplying both sides of the equation by 12 to eliminate the denominator of 12 and get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5t+=+12%29 ALIGN=MIDDLE  ALT=\"5t+=+12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve this equation by dividing both sides by 5:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+12%2F5 ALIGN=MIDDLE  ALT=\"t+=+12%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and divide 12 by 5 to get the answer:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+2.4 ALIGN=MIDDLE  ALT=\"t+=+2.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So it takes 2.4 hours for them working together to paint the house. (And since there are 60 minutes in an hour, the 0.4 of an hour is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2A0.4+=+24 ALIGN=MIDDLE  ALT=\"60%2A0.4+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" > minutes.) Therefore, working together they will complete the job in 2 hours and 24 minutes.<BR>\n" );
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document.write( "Hope this helps you to understand the problem better.<BR>\n" );
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