document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978734>Question 978734</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For a high school freshman orientation, the members of two clubs volunteer to set up tables in the gym. It takes 40 minutes for the math club alone and it takes 50 minutes for the science club alone. After the math club sets up the tables for 10 minutes, the science club joins. How long will it take them to finish 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 #600082 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=600082\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> math club takes 40 minutes<BR>\n" );
document.write( "science takes 50 minutes.<BR>\n" );
document.write( "rate * time = quantity<BR>\n" );
document.write( "quantity = 1 set up of the tables.<BR>\n" );
document.write( "rate for math club is 1/40 of all the tables in 1 minute.<BR>\n" );
document.write( "rate for science club is 1/50 of all the tables in 1 minute.<BR>\n" );
document.write( "math club works for 10 minutes.<BR>\n" );
document.write( "rate * time = quantity<BR>\n" );
document.write( "1/40 * 10 = 10/40 = 1/4 of the tables are already set up by the math club.<BR>\n" );
document.write( "there are 3/4 of the tables that still need to be set up.<BR>\n" );
document.write( "rate * time = quantity<BR>\n" );
document.write( "the rates of the math club and the science club are additive.<BR>\n" );
document.write( "(1/40 + 1/50) * time = 3/4 of the tables that still need to be set up.<BR>\n" );
document.write( "common denominator is 200.<BR>\n" );
document.write( "(5/200 + 4/200) * time = 3/4.<BR>\n" );
document.write( "9/200 * time = 3/4<BR>\n" );
document.write( "time = 3/4 * 200/9 = 600 / 36 = 16 and 2/3 minutes.<BR>\n" );
document.write( "total time required is 10 + 16 + 2/3 minutes = 26 + 2/3 minutes.<BR>\n" );
document.write( "how to check.<BR>\n" );
document.write( "10 minutes is used to do 1/4 of the tables.<BR>\n" );
document.write( "16 + 2/3 minutes is used to do the remaining 3/4 of the tables.<BR>\n" );
document.write( "combined rate of math and science club is 9/200 of the tables in 1 minute.<BR>\n" );
document.write( "math club rate of 1/40 * 10 = 10/40 = 1/4 of the tables.<BR>\n" );
document.write( "combine rate of 9/200 * (16 + 2/3) = 9/200 * 50/3 = 450/600 = 9/12 = 3/4 of the tables.<BR>\n" );
document.write( "1/4 + 3/4 = 1 = all of the tables.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );