document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1150748>Question 1150748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three workers have to do a certain job. The first worker can finish the job in 8 hours. The second worker can finish the job in 4 hours. The third worker can also finish the job in 4 hours. How long will it take the three workers to finish the job if they work together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #772173 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772173\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Tutor @ikleyn has shown the typical algebraic solution method for this kind of problem.<br><BR>\n" );
document.write( "Here are two alternative methods....<br><BR>\n" );
document.write( "(1) logical reasoning and some simple arithmetic....<br><BR>\n" );
document.write( "The worker who takes 8 hours to do the job alone takes twice as long as each of the others.  That means he works half as fast.<br><BR>\n" );
document.write( "So the three of them working together is like 2.5 workers working at the rate that it takes one of them to do the job alone.<br><BR>\n" );
document.write( "So the time it takes 2.5 workers to do the job at that rate is 4/2.5 = 8/5 hours.<br><BR>\n" );
document.write( "(2) using the least common multiple of the given times for the three workers....<br><BR>\n" );
document.write( "The numbers of hours for the three workers each to do the job alone are 8, 4, and 4.  The LCM of those numbers is 8.<br><BR>\n" );
document.write( "Consider what the three workers could do in 8 hours:<br><BR>\n" );
document.write( "The first worker could do the job once.<BR>\n" );
document.write( "The second worker could do the job 8/4 = 2 times.<BR>\n" );
document.write( "The third worker could do the job 8/4 = 2 times.<br><BR>\n" );
document.write( "So the three of them together in 8 hours could do the job 1+2+2=5 times.<br><BR>\n" );
document.write( "So the three of them can do the one job in 8/5 hours.<br>\r<BR>\n" );
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