document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=605210>Question 605210</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Luke,Eddie, and Ryan can complete a job in 1 hour and 20 minutes if they work together. Working alone, it take Ryan 1 hour more to complete the job than it takes Luke, and Luke works twice as fast as Eddie. How much time would it take each to complete the job working alone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #381575 by </B><A HREF=/tutors/aboutme.mpl?userid=alicealc><B>alicealc(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=alicealc><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=381575\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume there is 1 work, <BR>\n" );
document.write( "Luke alone can finish it in L hours,<BR>\n" );
document.write( "Eddie alone can finish it in E hours,<BR>\n" );
document.write( "Ryan alone can finish it in R hours,<BR>\n" );
document.write( "so,<BR>\n" );
document.write( "Luke's speed = 1/L<BR>\n" );
document.write( "Eddie's speed = 1/E<BR>\n" );
document.write( "Ryan's speed = 1/R\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Working alone, it take Ryan 1 hour more to complete the job than it takes Luke:<BR>\n" );
document.write( "R = 1 + L\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Luke works twice as fast as Eddie:<BR>\n" );
document.write( "1/L = 2 * 1/E<BR>\n" );
document.write( "1/L = 2/E<BR>\n" );
document.write( "E = 2L\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "working together:<BR>\n" );
document.write( "1 hour and 20 minutes = 1 20/60 hours = 1 1/3 hours = 4/3 hours<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FL+%2B+1%2FE+%2B+1%2FR+=+1%2F%284%2F3%29 ALIGN=MIDDLE  ALT=\"1%2FL+%2B+1%2FE+%2B+1%2FR+=+1%2F%284%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2FL+%2B+1%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29 ALIGN=MIDDLE  ALT=\"1%2FL+%2B+1%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%282L%29+%2B+1%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29 ALIGN=MIDDLE  ALT=\"2%2F%282L%29+%2B+1%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29 ALIGN=MIDDLE  ALT=\"3%2F%282L%29+%2B+1%2F%281%2BL%29+=+3%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A%281%2BL%29%2B1%2A2L%29%2F%28%282L%29%2A%281%2BL%29%29+=+3%2F4 ALIGN=MIDDLE  ALT=\"%283%2A%281%2BL%29%2B1%2A2L%29%2F%28%282L%29%2A%281%2BL%29%29+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B3L%2B2L%29%2F%282L%2B2L%5E2%29+=+3%2F4 ALIGN=MIDDLE  ALT=\"%283%2B3L%2B2L%29%2F%282L%2B2L%5E2%29+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B5L%29%2F%282L%2B2L%5E2%29+=+3%2F4 ALIGN=MIDDLE  ALT=\"%283%2B5L%29%2F%282L%2B2L%5E2%29+=+3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A%283+%2B+5L%29+=+3%2A%282L%2B2L%5E2%29 ALIGN=MIDDLE  ALT=\"4%2A%283+%2B+5L%29+=+3%2A%282L%2B2L%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2B20L+=+6L%2B6L%5E2 ALIGN=MIDDLE  ALT=\"12%2B20L+=+6L%2B6L%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+6L%5E2%2B6L-20L-12 ALIGN=MIDDLE  ALT=\"0+=+6L%5E2%2B6L-20L-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+6L%5E2-14L-12 ALIGN=MIDDLE  ALT=\"0+=+6L%5E2-14L-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(divide all by 2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+3L%5E2-7L-6 ALIGN=MIDDLE  ALT=\"0+=+3L%5E2-7L-6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "0 = (3L + 2)*(L - 3)<BR>\n" );
document.write( "3L + 2 = 0 or L - 3 = 0<BR>\n" );
document.write( "3L = -2 or L = 3<BR>\n" );
document.write( "L = -2/3 or L = 3<BR>\n" );
document.write( "because the time can't be a negative number, we choose L = 3<BR>\n" );
document.write( "R = 1 + L = 1 + 3 = 4<BR>\n" );
document.write( "E = 2L = 2 * 3 = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so,<BR>\n" );
document.write( "Luke alone takes 3 hours to complete the job<BR>\n" );
document.write( "Ryan alone takes 4 hours to complete the job<BR>\n" );
document.write( "Eddie alone takes 6 hours to complete the job<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );