document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=699066>Question 699066</A>: <I><SPAN STYLE=\"word-break: break-all;\"> \"This is the problem. Would you please help me with this? Thank You!\" ---> A and B working together can finish a certain job in 20/3 hours. They start the work together but after 3 hours. A became ill and B continuing the work alone finished it in 33/4 hours. How long would it take each working alone to do the job? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431291 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=431291\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A and B working together can finish a certain job in 20/3 hours.<BR>\n" );
document.write( " They start the work together, but after 3 hours, A became ill and B continuing the work alone. finished it in 33/4 hours.<BR>\n" );
document.write( " How long would it take each working alone to do the job?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let a = A doing the job alone<BR>\n" );
document.write( "let b = B doing it alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a share work equation for the statement:<BR>\n" );
document.write( "\"A and B working together can finish a certain job in 20/3 hours.\"<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2F3%29%2Fa ALIGN=MIDDLE  ALT=\"%2820%2F3%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820%2F3%29%2Fb ALIGN=MIDDLE  ALT=\"%2820%2F3%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "invert the divisor and multiply<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%283a%29 ALIGN=MIDDLE  ALT=\"20%2F%283a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%2F%283b%29 ALIGN=MIDDLE  ALT=\"20%2F%283b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by 3ab, results<BR>\n" );
document.write( "20b + 20a = 3ab<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" They start the work together but after 3 hours, A became ill and B continuing the work alone, finished it in 33/4 hours. How long would it take each working alone to do the job?\"<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Change 33/4 hrs to 8.25 hrs<BR>\n" );
document.write( "B works 3 + 8.25 = 11.25 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Fa ALIGN=MIDDLE  ALT=\"3%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.25%2Fb ALIGN=MIDDLE  ALT=\"11.25%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by ab to clear the denominators<BR>\n" );
document.write( "3b + 11.25a = ab<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Try to use elimination with these two equations<BR>\n" );
document.write( "3b + 11.25a = ab<BR>\n" );
document.write( "20b + 20a = 3ab<BR>\n" );
document.write( "Multiply the 1st equation by 20, multiply the 2nd equation by 3<BR>\n" );
document.write( "60b + 225a = 20ab<BR>\n" );
document.write( "60b + 60a = 9ab<BR>\n" );
document.write( "-----------------subtraction eliminates b<BR>\n" );
document.write( "165a = 11ab<BR>\n" );
document.write( "divide both side by a<BR>\n" );
document.write( "165 = 11b<BR>\n" );
document.write( "b = 165/11<BR>\n" );
document.write( "b = 11 hrs working alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find a, <BR>\n" );
document.write( "20b + 20a = 3ab<BR>\n" );
document.write( "replace b with 11<BR>\n" );
document.write( "20(11) + 20a = 3(a*11)<BR>\n" );
document.write( "220 + 20a = 33a<BR>\n" );
document.write( "220 = 33a - 20a<BR>\n" );
document.write( "220 = 13a<BR>\n" );
document.write( "a = 220/13<BR>\n" );
document.write( "a = 16<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2F13 ALIGN=MIDDLE  ALT=\"12%2F13\"   DISABLED_style= \"max-width:90%; height:auto;\" > hrs working alone <BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this in the 1st work statement equation but we will use decimals instead of those annoying fractions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.67%2F16.92 ALIGN=MIDDLE  ALT=\"6.67%2F16.92\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.67%2F11 ALIGN=MIDDLE  ALT=\"6.67%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <BR>\n" );
document.write( ".394 + .606 = 1; confirms our solutions\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );