document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=490937>Question 490937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Mary can paint a house in 4 hours and it takes John 6 hours to paint the same house, how long would it take them if they worked together? The answer is 2 hours and 44 minutes.  I just cannot get there...HELP!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334369 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=334369\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = units<BR>\n" );
document.write( "the unit is equal to 1 (the house).<BR>\n" );
document.write( "mary can paint the house in 4 hours.<BR>\n" );
document.write( "for mary, the equation becomes:<BR>\n" );
document.write( "rate * 4 = 1<BR>\n" );
document.write( "solve for rate to get mary's rate = 1/4<BR>\n" );
document.write( "this means that mary can paint 1/4 of the house in 1 hour.\r<BR>\n" );
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document.write( "for john the equation becomes:<BR>\n" );
document.write( "rate * 6 = 1<BR>\n" );
document.write( "solve for rate to get john's rate = 1/6<BR>\n" );
document.write( "this means that john can paint 1/6 of the house in 1 hour.\r<BR>\n" );
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document.write( "you want to know how long it takes them to paint the house together.<BR>\n" );
document.write( "if they paint the house together, then their rates are additive.<BR>\n" );
document.write( "the equation you get is:\r<BR>\n" );
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document.write( "(1/4 + 1/6) * time = 1<BR>\n" );
document.write( "the unit is still one.<BR>\n" );
document.write( "you have the rates for mary and john that you are adding together.<BR>\n" );
document.write( "now you are solving for time.\r<BR>\n" );
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document.write( "you get:<BR>\n" );
document.write( "(1/4 + 1/6) * time = 1<BR>\n" );
document.write( "this is equivalent to:<BR>\n" );
document.write( "(3/12 + 2/12) * time = 1<BR>\n" );
document.write( "this is equivalent to:<BR>\n" );
document.write( "(5/12) * time = 1<BR>\n" );
document.write( "divide both sides of the equation by (5/12) to get:<BR>\n" );
document.write( "time = 1 / (5/12)<BR>\n" );
document.write( "this is equivalent to:<BR>\n" );
document.write( "time = 1 * (12/5) which is equivalent to:<BR>\n" );
document.write( "time = 12/5 which is equivalent to:<BR>\n" );
document.write( "time = 2.4 hours.\r<BR>\n" );
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document.write( "this is NOT equivalent to 2 hours and 44 minutes.<BR>\n" );
document.write( "it is equivalent to 2 hours and 24 minutes.<BR>\n" );
document.write( ".4 * 60 = 24 minutes.\r<BR>\n" );
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document.write( "let's see if the answer makes sense.<BR>\n" );
document.write( "mary works for 2.4 hours so she paints 1/4 * 2.4 = .6 of the house.<BR>\n" );
document.write( "john works for 2.4 hours so he paints 1/6 * 2.4 = .4 of the house.<BR>\n" );
document.write( "together they paint .6 + .4 = 1 of the house.<BR>\n" );
document.write( "1 of the house is the whole house, so they are done and the values for the time it takes are also good.\r<BR>\n" );
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document.write( "i don't know where you got 2 hours and 44 minutes from but it is not correct for this problem.\r<BR>\n" );
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document.write( "it should be 2 hours and 24 minutes.\r<BR>\n" );
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document.write( "2 hours and 24 minutes is equal to 2 + 24/60 = 2 + .4 = 2.4 hours which is correct.\r<BR>\n" );
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document.write( "2 hours and 44 minutes is equal to 2 + 44/60 = 2 + .733333333 = 2.73333333 hours which would not be correct.\r<BR>\n" );
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document.write( "check the problem and the answer that it should be again to make sure you are dealing with the right numbers.\r<BR>\n" );
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document.write( "if the problem is as you stated and the answer is as you stated, then there's something wrong with the way the problem has been presented.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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