document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166226>Question 1166226</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have tried to solve this, and got an answer of \"1.14 days\". <BR>\n" );
document.write( "But, I am a little bit confused...So, can you please help me with this.<BR>\n" );
document.write( "Ana can finish her research project in 6 days and her parner can finish in 8 days, after working for three days, Ana's partner joined her, how long would it take to finish the project </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790704 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=790704\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "the basic formula is r * t = q<BR>\n" );
document.write( "r is the rate<BR>\n" );
document.write( "t is the time<BR>\n" );
document.write( "q is the quantity of work produced\r<BR>\n" );
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document.write( "when 2 people work together, their rates are additive.<BR>\n" );
document.write( "the formula then becomes (r1 + r2) * t = q\r<BR>\n" );
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document.write( "when they work alone for the entire project, q becomes 1 because we have defined the quantity of work as completion of one project.\r<BR>\n" );
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document.write( "for ana, the formula becomes r * t = 1<BR>\n" );
document.write( "for her partner, the formula becomes r * t = 1\r<BR>\n" );
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document.write( "since ana can complete the project in 6 days, her formula becomes r * 6 = 1.<BR>\n" );
document.write( "solve for r to get r = 1/6.<BR>\n" );
document.write( "this means ana can complete 1/6 of the job in 1 day.\r<BR>\n" );
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document.write( "since her partner can complete the project in 8 days, her formula becomes r * 8 = 1.<BR>\n" );
document.write( "solve for r to get r = 1/8.<BR>\n" );
document.write( "this means her partner can complete 1/8 of the job in 1 day.\r<BR>\n" );
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document.write( "you are given that ana worked alone for 3 days.<BR>\n" );
document.write( "since she can complete 1/6 of the job in 1 day, then she can complete 3/6 of the job in 3 days.<BR>\n" );
document.write( "r * t = q becomes 1/6 * 3 = q which becomes q = 1/2\r<BR>\n" );
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document.write( "ana has completed half of the job when her partner joins her.<BR>\n" );
document.write( "they work together to complete the other half of the job.\r<BR>\n" );
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document.write( "they're working together, so (r1 + r2) * t = q becomes (1/6 + 1/8) * t = 1/2<BR>\n" );
document.write( "q becomes 1/2 because 1/2 of the job remains to be done.\r<BR>\n" );
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document.write( "this becomes (1/6 + 1/8) * t = 1/2<BR>\n" );
document.write( "a common denominator is 24, so the formula becomes:<BR>\n" );
document.write( "(4/24 + 3/24) * t = 1/2<BR>\n" );
document.write( "combine like terms to get 7/24 * t = 1/2<BR>\n" );
document.write( "multiply both sides of this formula by 2 to get:<BR>\n" );
document.write( "14/ * t = 1<BR>\n" );
document.write( "solve for t to get:<BR>\n" );
document.write( "t = 24/14 * 1 = 1 and 10/14 days.<BR>\n" );
document.write( "this simplifies to 1 and 5/7 days.\r<BR>\n" );
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document.write( "place into decimal format and the answer is 1.714285714 days.\r<BR>\n" );
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document.write( "that should be your solution. ******************************************\r<BR>\n" );
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document.write( "add 3 days that ana worked on her own and the total time it took to finish the job ws 4.714285714 days.\r<BR>\n" );
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document.write( "your solution should be 1.714285714 days. ******************************\r<BR>\n" );
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document.write( "if you worked in decimal, then you should have gotten.<BR>\n" );
document.write( "ana's rate is 1/6.<BR>\n" );
document.write( "her partner's rate is 1/8.<BR>\n" );
document.write( "in 3 hours ana completed 1/6 * 3 = 1/2 of the job = .5<BR>\n" );
document.write( "when they worked together, (1/6 + 1/8) * t = .5<BR>\n" );
document.write( "this becomes .29166666... * t = .5<BR>\n" );
document.write( "solve for t to get t = .5 / .2916666..... = 1.714285714 days.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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