document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204620>Question 1204620</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hot water tap can fill the tub in 10 minutes. The cold water tap can fill the tub in 8 minutes. How long would it take to fill the tub if both taps are opened? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840981 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=840981\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "This kind of \"working together\" problem, with two workers working at different rates, is so common that it might be useful to learn the short answer:<br><BR>\n" );
document.write( "If two workers alone take A hours and B hours to complete a job, then the number of hours it takes them to do the job together is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28AB%29%2F%28A%2BB%29 ALIGN=MIDDLE  ALT=\"%28AB%29%2F%28A%2BB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Of course the unit of time is not relevant -- it could be minutes, or years, or milliseconds....<br><BR>\n" );
document.write( "So for this problem the quick answer is 80/18 = 40/9 minutes.<br><BR>\n" );
document.write( "For another easy way to solve this kind of problem, consider the least common multiple of the two given times.  For this problem, with the two times being 10 and 8 minutes, the least common multiple is 40 minutes.<br><BR>\n" );
document.write( "Now consider the amount of work the two taps could do in 40 minutes.  The hot water tap could fill the tub 40/10 = 4 times; the cold water tap could fill the tub 40/8 = 5 times.<br><BR>\n" );
document.write( "So in 40 minutes the two taps together could fill the tub 4+5 = 9 times; so the number of minutes it takes them together to fill the one tub is 40/9.<br><BR>\n" );
document.write( "ANSWER: 40/9 minutes<br><BR>\n" );
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