document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172530>Question 1172530</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Theresa can do a piece of work in 15 days. After she has worked 3 days, Rowena joins her and they finish work in 4 days. How long can Rowena finish the work alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797593 by </B><A HREF=/tutors/aboutme.mpl?userid=VFBundy><B>VFBundy(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=VFBundy><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=VFBundy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=797593\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> After 3 days, Theresa has completed 3/15 (or 1/5) of the work.  This means there is 4/5 of the work remaining.<BR>\n" );
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document.write( "So, working together, Theresa and Rowena can complete 4/5 of the work in 4 days.<BR>\n" );
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document.write( "Theresa's rate of work is: 1/15 of the work per day.<BR>\n" );
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document.write( "Rowena's rate of work is: 1/x of the work per day.<BR>\n" );
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document.write( "Rate of both working together: 1/15 + 1/x = x/15x + 15/15x = (x + 15)/15x of the work per day.<BR>\n" );
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document.write( "Rate of Work TIMES Days of Work = Total work<BR>\n" );
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document.write( "[(x + 15)/15x] * 4 = 4/5<BR>\n" );
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document.write( "4(x + 15)/15x = 4/5<BR>\n" );
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document.write( "(4x + 60)/15x = 4/5<BR>\n" );
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document.write( "5(4x + 60) = 4(15x)<BR>\n" );
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document.write( "20x + 300 = 60x<BR>\n" );
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document.write( "-40x = -300<BR>\n" );
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document.write( "x = 15/2<BR>\n" );
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document.write( "That means it would have taken Rowena 15/2 days (or, 7.5 days) to do the ENTIRE work alone.  However, since 1/5 of the work was already done by Theresa, only 4/5 of the work remains.  That means it will take Rowena (4/5 * 15/2) days to FINISH the work alone.  4/5 * 15/2 = 60/10 = 6.  <b>Therefore, it will take Rowena 6 days to finish the remaining work alone.</b> <BR>\n" );
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document.write( "**NOTE: The question specifically asks how long it will take Rowena to FINISH the work, implying it is asking how long it will take her to complete the work AFTER the work by Theresa has already been done. </SPAN>\n" );
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