document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198854>Question 1198854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Quiboy can clean the barn in 6 hours, and Quiboy and Rod together can clean the same barn in 3 hours. How long would it take for Rod to clean the barn by himself? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832532 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832532\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The jump from 6 hours to 3 hours is \"times 1/2\".\r<BR>\n" );
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document.write( "This strongly suggests the two people work at the same rate, and take the same amount of time. <BR>\n" );
document.write( "This is because they split the work in half (thereby cutting their worktime in half as well).\r<BR>\n" );
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document.write( "We can think of it like saying the task is to move 60 bales of hay.<BR>\n" );
document.write( "Quiboy needs 6 hours to do the job by himself. <BR>\n" );
document.write( "His unit rate is 60/6 = 10 bales per hour.\r<BR>\n" );
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document.write( "When working together, the two men can do the job in 3 hours. <BR>\n" );
document.write( "Their combined rate is 60/3 = 20 bales per hour.<BR>\n" );
document.write( "This of course assumes neither worker hinders the other.\r<BR>\n" );
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document.write( "Quiboy offers 10 bales per hour, and the total combined rate is 20 bales per hour. <BR>\n" );
document.write( "Rod offers the remaining 20-10 = 10 bales per hour. <BR>\n" );
document.write( "His rate is the same as Quiboy. So he takes the same amount of time.\r<BR>\n" );
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document.write( "If you wish to use algebra, then,<BR>\n" );
document.write( "x = time (in hours) needed for Rod to do the job alone\r<BR>\n" );
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document.write( "1/6 = Quiboy's unit rate<BR>\n" );
document.write( "1/x = Rod's unit rate<BR>\n" );
document.write( "1/3 = combined unit rate\r<BR>\n" );
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document.write( "1/6 + 1/x = 1/3<BR>\n" );
document.write( "x/(6x) + 6/(6x) = 1/3<BR>\n" );
document.write( "(x+6)/(6x) = 1/3<BR>\n" );
document.write( "3(x+6) = 6x*1<BR>\n" );
document.write( "3x+18 = 6x<BR>\n" );
document.write( "18 = 6x-3x<BR>\n" );
document.write( "18 = 3x<BR>\n" );
document.write( "3x = 18<BR>\n" );
document.write( "x = 18/3<BR>\n" );
document.write( "x = 6\r<BR>\n" );
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document.write( "Or you could say<BR>\n" );
document.write( "1/6 + 1/x = 1/3<BR>\n" );
document.write( "6x * ( 1/6+1/x ) = 6x*( 1/3 )<BR>\n" );
document.write( "6x*(1/6) + 6x*(1/x) = 6x*( 1/3 )<BR>\n" );
document.write( "x + 6 = 2x<BR>\n" );
document.write( "6 = 2x-x<BR>\n" );
document.write( "6 = x<BR>\n" );
document.write( "x = 6\r<BR>\n" );
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document.write( "In my opinion an algebraic approach is a bit overkill. <BR>\n" );
document.write( "Despite that, it's still handy to know this pathway and get practice.\r<BR>\n" );
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document.write( "Answer: 6 hours<BR>\n" );
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