document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199268>Question 1199268</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Jay can do a painting job in 2/3 as many days as Chris can, and Chris can do it in 3/4 as many days as Araceli can. If all three work together, they can do it in 36/13 days. In how many days can each of them alone do the work?                      </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833062 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=833062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Jay can do a painting job in 2/3 as many days as Chris can,<BR>\n" );
document.write( " and Chris can do it in 3/4 as many days as Araceli can.<BR>\n" );
document.write( " If all three work together, they can do it in 36/13 days.<BR>\n" );
document.write( " In how many days can each of them alone do the work?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let a = time required by A do the job<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(2/3)*(3/4) = (1/2)a = J's time to do the job<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(3/4)a = C's time<BR>\n" );
document.write( "We can use decimals with these two fractions, .5 and .75 (less tedious)<BR>\n" );
document.write( "lets try using 36/13 = 2.77 for time working together<BR>\n" );
document.write( "let 1 = the completed job<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.77%2F%28.5a%29 ALIGN=MIDDLE  ALT=\"2.77%2F%28.5a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.77%2F%28.75a%29 ALIGN=MIDDLE  ALT=\"2.77%2F%28.75a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.77%2Fa ALIGN=MIDDLE  ALT=\"2.77%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1 <BR>\n" );
document.write( "multiply by 3a, cancel the denominators, gets rid of the fractions <BR>\n" );
document.write( "6(2.77) + 4(2.77) + 3(2.77) = 3a <BR>\n" );
document.write( "16.62 + 11.08 + 8.31 = 3a<BR>\n" );
document.write( "totals 36.01,round it down to 36<BR>\n" );
document.write( "3a = 36<BR>\n" );
document.write( "a = 12 hrs is A's time<BR>\n" );
document.write( "then<BR>\n" );
document.write( ".5(12) = 6 hrs is J's time<BR>\n" );
document.write( "and<BR>\n" );
document.write( ".75(12) = 9 hrs is C's time<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can confirm this in the original equation, comes to slightly more than 1 because 2.77 is actually 2.76923 (36/13)<BR>\n" );
document.write( "  </SPAN>\n" );
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