document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=829334>Question 829334</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bart can peel a batch of 3000 lbs of apples in 12 hours with an old machine, while Mona can do the same job in 8 hrs using the new machine. If Bart starts peeling at 8am and Mona joins him at 9am then at what time will they finish the batch working together. So far I have 1/t1+1/t2=1/t3 so that is 1/12+1/8=1/x<BR>\n" );
document.write( "2x+3x=24<BR>\n" );
document.write( "6x=24<BR>\n" );
document.write( "x=4 but I am clueless as to what I am supposed to do with the extra hour Bart has? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #499793 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=499793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's start from here, the correct equation for their combined rate: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F12%2B1%2F8=1%2Fx ALIGN=MIDDLE  ALT=\"1%2F12%2B1%2F8=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F24%2B3%2F24=1%2Fx ALIGN=MIDDLE  ALT=\"2%2F24%2B3%2F24=1%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" >... but instead of solving for x, just compute the rate.  That is what you really want, even if it is as a rational number, fraction form.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%285%2F24%29 ALIGN=MIDDLE  ALT=\"highlight_green%285%2F24%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > batches per hour.<BR>\n" );
document.write( "You can also say, 5 batchs in 24 hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Next, look at time values, not necessarily viewed on a number line.  Time 8AM is time, ZERO.  Let h be the time after the first hour, because Mona joins Bart after ONE hour.  Bart works for 1+h hours and Mona works with him for h hours.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The total jobs done will be 1.<BR>\n" );
document.write( "This one job is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=jobByBart%2BjobByBoth=1 ALIGN=MIDDLE  ALT=\"jobByBart%2BjobByBoth=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28highlight%28%281%2F12%29%2A1%2B%285%2F24%29%28h%2B1%29=1%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28highlight%28%281%2F12%29%2A1%2B%285%2F24%29%28h%2B1%29=1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "Most important is to understand the analysis, and the resulting equation.  Solving it for h should be much less of a chore. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );