document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=644146>Question 644146</A>: <I><SPAN STYLE=\"word-break: break-all;\"> one pipe can fill a pool 1.25 times faster than a second pipe . When both pipes are opened , they fill the pool in five hours . How long would it take to fill the pool if only the slower pipe is used ? tanx<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #404849 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=404849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r1 = flow rate of slower pipe <BR>\n" );
document.write( "Let r2 = flow rate of faster pipe<BR>\n" );
document.write( "Let G = the capacity of the pool<BR>\n" );
document.write( "Knowns:<BR>\n" );
document.write( "1) faster rate = 1.25 slower rate.<BR>\n" );
document.write( "2) It takes 5 hours to fill the pool with both pipes.<BR>\n" );
document.write( "Unknowns:<BR>\n" );
document.write( "a) The time, T. to fill pool at the slower flow rate.<BR>\n" );
document.write( "Appropriate formula to use:<BR>\n" );
document.write( "G = r*t, where G is capacity in gallons, r is the rate of flow in gal/hr and t is the time in hours.<BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "With both pipes flowing, we have<BR>\n" );
document.write( "(1) G = (r1 + r2)*5<BR>\n" );
document.write( "Substituting the knowns into (1) yields<BR>\n" );
document.write( "(2) G = (r1 + 1.25*r1)*5<BR>\n" );
document.write( "Simplifying (2), we get<BR>\n" );
document.write( "(3) G = r1*(1 + 1.25)*5 or<BR>\n" );
document.write( "(4) G = 2.25*5*r1 or<BR>\n" );
document.write( "(5) G = 11.25*r1<BR>\n" );
document.write( "Filling the pool with just at the slow rate, is given by<BR>\n" );
document.write( "(6) G = r1*T<BR>\n" );
document.write( "Setting G of (5) equal to the same G of (6) yields<BR>\n" );
document.write( "(7) G = G  or<BR>\n" );
document.write( "(8) 11.25*r1 = r1*T<BR>\n" );
document.write( "The r1 factor on LS cancels r1 on the RS, leaving only<BR>\n" );
document.write( "(9) T = 11.25 hrs<BR>\n" );
document.write( "We should always check our answer. Any idea of how can we check this value of time T? Let me ask you,\"Is r2 = 1.25*r1?\"<BR>\n" );
document.write( "Let's find r1 and r2.<BR>\n" );
document.write( "In (5) we have<BR>\n" );
document.write( "(10) r1 = G/11.25<BR>\n" );
document.write( "From (2) we have<BR>\n" );
document.write( "(11) r1 + r2 = G/5<BR>\n" );
document.write( "Now substitute (10) into (11) to get<BR>\n" );
document.write( "(12) r2 = G/5 - G/11.25 or<BR>\n" );
document.write( "(13) r2 = ((11.25 - 5)/(5*11.25))*G or<BR>\n" );
document.write( "(14) r2 = (6.25/(5*11.25))*G or<BR>\n" );
document.write( "(15) r2 = 125/1125*G or<BR>\n" );
document.write( "(16) r2 = G/9<BR>\n" );
document.write( "Now <BR>\n" );
document.write( "Is (r2 = 1.25*r1)?<BR>\n" );
document.write( "Is (G/9 = 1.25*(G/11.25))?<BR>\n" );
document.write( "Is (G/9 = G/9)?<BR>\n" );
document.write( "Is (9 = 9)? Yes <BR>\n" );
document.write( "Answer: The pipe with the slower flow rate will take 11.25 hours to fill the pool. </SPAN>\n" );
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