document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208808>Question 1208808</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A tub can be filled with hot water in 18 minutes, or with cold water in 12 minutes. The tub can also be emptied when the plug is pulled out, in 9 minutes. Farley ran the hot water in his tub for 8 minutes, then both the cold and hot water together for 2 minutes, and then with the two taps still running, he accidentally pulled the plug. How long did it take, in minutes, for the tub to fill after the plug was pulled?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847267 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13208)</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=847267\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The fraction of the tub filled in 1 minute by the hot water tap alone is 1/18.<br><BR>\n" );
document.write( "The fraction of the tub filled in 1 minute by both taps together is 1/18 + 1/12 = 2/36 + 3/36 = 5/36.<br><BR>\n" );
document.write( "The fraction of the tub drained by the drain in 1 minute is 1/9.<br><BR>\n" );
document.write( "When both taps and the drain are all open, the fraction of the tub filled in 1 minute is 5/36 - 1/9 = 5/36 - 4/36 = 1/36.<br><BR>\n" );
document.write( "The hot water tap is run for 8 minutes.  The fraction of the tub filled is 8(1/18) = 8/18 = 4/9.<br><BR>\n" );
document.write( "Both taps are run for 2 minutes.  The fraction of the tub filled in those 2 minutes is 2(5/36) = 10/36 = 5/18.  The fraction of the tub now filled is 4/9 + 5/18 = 8/18 + 5/18 = 13/18; the fraction of the tub remaining to be filled is 5/18.<br><BR>\n" );
document.write( "The fraction of the tub remaining to be filled is 5/18; the rate at which the tub is being filled with both taps and the drain all open is 1/36.  The number of minutes needed to finish filling the tank after the drain is opened is (5/18)/(1/36) = (10/36)/(1/36) = 10.<br><BR>\n" );
document.write( "ANSWER: 10 minutes<br><BR>\n" );
document.write( "CHECK:<BR>\n" );
document.write( "The hot water tap will have been running for 8+2+10 = 20 minutes; the cold water tap for 2+10 = 12 minutes; and the drain will have been open for 10 minutes.  The tub should be full at the end of that time -- i.e, the fraction of the tub that should be full is 1.<br><BR>\n" );
document.write( "20(1/18) + 12(1/12) - 10(1/9) = 20/18 + 1 - 10/9 = 1<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );