document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1011393>Question 1011393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Chynna can type a report in 5 hours. Bea, who is a slow typist, helped Chynna and together, they finished the report within 3 hours. How long would it take for Bea has she worked alone. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #627040 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=627040\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = quantity of work produced.<BR>\n" );
document.write( "quantity of work produced / rate = time it takes to produce the work.<BR>\n" );
document.write( "quantity of work / time = how much of the work is being produced per unit of time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the quantity of work is 1 paper.<BR>\n" );
document.write( "the time for chynna is 5  hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "chynna can type the report in 5 hours.<BR>\n" );
document.write( "rate * time = quantity of work becomes rate * 5 = 1<BR>\n" );
document.write( "solve for rate to get rate = 1/5<BR>\n" );
document.write( "chynna can type 1/5 of the paper each hour that she works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "bea helps chynna and they can finish the report in 3 hours.<BR>\n" );
document.write( "when bea helps chynna, their rates are additive.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "let x = the rate that bea works at.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "rate * time = quantity becomes (1/5 + x) * 3 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "distribute the multiplication to get 3/5 + 3x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "subtract 3/5 from both sides of the equation to get 3x = 1 - 3/5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get 3x = 2/5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of this equation by 3 to get x = 2/15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the rate that bea works at is 2/15 of the report for each hour that she works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if we let x = time it takes bea if she works alone, the rate * time = quantity of work produced equation becomes 2/15 * x = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for x to get x = 15/2 hours = 7.5 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "bea can finish the job herself in 7.5 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "for bea, the rate * time = quantity of work produced equation becomes 2/15 * 7.5 = 1 which becomes 15/15 = 1 which becomes 1 = 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this confirms the solution is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "also confirming would be when bea and chynna work together.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the rate * time equation becomes (1/5 + 2/15) * 3 = 1\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since 1/5 = 3/15, this equation becomes (3/15 + 2/15) * 3 = 1 which becomes 5/15 * 3 = 1 which becomes 15/15 = 1 which becomes 1 = 1.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that equation is confirmed to be correct as well when bea's rate is 2/15 of the paper per hour.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "answer to your question is that it would take bea 7.5 hours to type the report by herself.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );