document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150509>Question 150509</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1592009425/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them 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 #110489 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=110489\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> working together, alice and betty can do a certain job in 4 1/3 days. but alice fell ill after 2 days of working and betty finished the job continuing to work alone in 6 3/4 more days. how long would it take each to do the job if each of them worked alone?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let a = time required by Alice working alone<BR>\n" );
document.write( "Let b = time required by Betty alone<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "equation when they both work 4<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > day<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.33%2Fa ALIGN=MIDDLE  ALT=\"4.33%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.33%2Fb ALIGN=MIDDLE  ALT=\"4.33%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by 3 give us integers to work with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fb ALIGN=MIDDLE  ALT=\"13%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Equation when one got sick; (b worked a total of 2+6.75 = 8.75<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fa ALIGN=MIDDLE  ALT=\"2%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.75%2Fb ALIGN=MIDDLE  ALT=\"8.75%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply equation by 6.5 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56.875%2Fb ALIGN=MIDDLE  ALT=\"56.875%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use elimination here:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=56.875%2Fb ALIGN=MIDDLE  ALT=\"56.875%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fb ALIGN=MIDDLE  ALT=\"13%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( "-------------------------------subtraction eliminates a, find b<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43.875%2Fb ALIGN=MIDDLE  ALT=\"43.875%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3.5<BR>\n" );
document.write( "3.5b = 43.875<BR>\n" );
document.write( "b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=43.75%2F3.5 ALIGN=MIDDLE  ALT=\"43.75%2F3.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b = 12.5357 days for Betty alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fb ALIGN=MIDDLE  ALT=\"13%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3, substitute for b and find a<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F12.5357 ALIGN=MIDDLE  ALT=\"13%2F12.5357\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1.037 = 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3 - 1.037<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2Fa ALIGN=MIDDLE  ALT=\"13%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.963<BR>\n" );
document.write( "1.963a = 13<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13%2F1.963 ALIGN=MIDDLE  ALT=\"13%2F1.963\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = 6.6225 days for Alice alone<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":<BR>\n" );
document.write( "To check solutions, use <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Fa ALIGN=MIDDLE  ALT=\"2%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.75%2Fb ALIGN=MIDDLE  ALT=\"8.75%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1, substituting for a and b:<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F6.6225 ALIGN=MIDDLE  ALT=\"2%2F6.6225\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8.75%2F12.5357 ALIGN=MIDDLE  ALT=\"8.75%2F12.5357\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( ".302 + .698 = 1; confirms our solution <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );