document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=862331>Question 862331</A>: <I><SPAN STYLE=\"word-break: break-all;\"> math question - a hose can fill a swimming pool in 50 minutes. the pool leaks at a steady rate that drains completely in 300 minutes, how many minutes will it take the hose to fill the leaky pool? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #519610 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=519610\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the equation to use is RT=Q<BR>\n" );
document.write( "this means rate * time = quantity of work produced.<BR>\n" );
document.write( "Q = 1 which is 1 pool<BR>\n" );
document.write( "to fill the pool, the equation is R*50 = 1 which makes R = 1/50.<BR>\n" );
document.write( "the pool fills at the rate of 1/50 of the pool each minute.<BR>\n" );
document.write( "to empty the pool, the equation is R*300 = 1 which makes R = 1/300.<BR>\n" );
document.write( "the pool empties at the rate of 1/300 of the pool each minute.<BR>\n" );
document.write( "if you start with an empty pool, then for each minute, 1/50 of the pool will be filled and 1/300 of the pool will be emptied, assuming the fill and empty rates stay the same throughout.<BR>\n" );
document.write( "that's a net fill rate of 1/50 - 1/300 which is equal to 6/300 - 1/300 which is equal to 5/300.<BR>\n" );
document.write( "for net fill rate is therefore 5/300 of the pool per minute.<BR>\n" );
document.write( "the same equation applies, only this time R is known and we can solve for T.<BR>\n" );
document.write( "5/300 * T = 1 is the equation we start with:<BR>\n" );
document.write( "multiply booth sides of this equation by 300 to get 5 * T = 300<BR>\n" );
document.write( "divide both sides of this equation by 5 to get T = 300/5 = 60 minutes.<BR>\n" );
document.write( "the pool will be filled in 60 minutes.<BR>\n" );
document.write( "since T = 60 minutes, the gross fill rate is 1/50 of the pool per minute to make 60/50 of the pool full in 60 minutes, and the gross empty rate is 1/300 of the pool per minute to make 60/300 of the pool empty in 60 minutes.<BR>\n" );
document.write( "60/50 - 60/300 = 360 / 300 - 60/300 = 300/300 = 1.<BR>\n" );
document.write( "the net effect of filling at the rate of 1/50 of the pool per minute and emptying at the rate of 1/300 of the pool per minute gets you 1 full pool after 60 minutes.<BR>\n" );
document.write( " </SPAN>\n" );
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