document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=386918>Question 386918</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ben can paint a fence in 3hrs and billy takes 4hrs. How long will it take them painting together? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #273592 by </B><A HREF=/tutors/aboutme.mpl?userid=Jk22><B>Jk22(389)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Jk22><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=Jk22><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=273592\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> we have : 3h=L/v_ben, and 4h=L/v_bil, where L is the length, v_x is the painting speed of x.\r<BR>\n" );
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document.write( "If they paint together : L_ben+L_bil=L=t(v_ben+v_bil)=t(L/3+L/4)<BR>\n" );
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document.write( "hence the time needed is : t = L/(L/3+L/4)=1/(1/3+/4)=12/7 hours, or 1.71 hours, which is half of the harmonic mean. It's parallel working, so the same formula as in electronics with resistance.<BR>\n" );
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document.write( "check : with the speed of painting : 12/7*L/3+12/7*L/4=L*12/7*(1/3+1/4)=L*12/7*7/12=L, which is the total length to be paint.\r<BR>\n" );
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