document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=374925>Question 374925</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes John 20 hours to paint a building. It takes Sam 15 hours to paint the same building. How long will it take for them to paint the building if they work together, with Sam starting one hour later than John? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266620 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=266620\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "If A can do a job in <i>x</i> time periods, then A can do <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{x}\"> of the job in 1 time period.  Likewise, if B can do the same job in <i>y</i> time periods, then B can do <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{y}\"> of the job in 1 time period.\r<BR>\n" );
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document.write( "So, working together, they can do\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{1}{x}\ +\ \frac{1}{y}\ =\ \frac{x\ +\ y}{xy} \">\r<BR>\n" );
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document.write( "of the job in 1 time period.\r<BR>\n" );
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document.write( "Therefore, they can do the whole job in:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  \frac{1}{\frac{x + y}{xy}}\ =\ \frac{xy}{x\ +\ y}\">\r<BR>\n" );
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document.write( "time periods.\r<BR>\n" );
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document.write( "However, since John has been working for an hour before Sam starts to help him, John has completed <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{1}{20}\"> of the job already.  That means that there are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{19}{20}\"> of the job remaining when Sam starts.  If it takes Sam 15 hours to do the entire job by himself, then it would take him <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{19}{20}\ \times\ 15\ =\ \frac{57}{4}\"> hours to do the remaining part of the job by himself.  And quite obviously it would take John 19 hours to finish by himself.\r<BR>\n" );
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document.write( "So just do the process outlined using <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 19\"> hours and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{57}{4}\"> hours as the times for the whole job.  And don't forget to add back the hour that John has already been working.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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