document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211575>Question 211575</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780495558880/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with this \"filling storage tanks\" word problem? Two pipes ure used to fill a water storage tank. The first pipe can fill the tank in 4hrs, and the two pipes together can fill the tank in 2 hrs less time than the second pipe alone. How long would it take for the second pipe to fill the tank? please show me all the steps and please get back before Tues 10am. <BR>\n" );
document.write( "Thanks guys </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159882 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=159882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = number of gallons filled<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "r1 = hose 1 rate<BR>\n" );
document.write( "t1 = hose 1 time<BR>\n" );
document.write( "r2 = hose 2 rate<BR>\n" );
document.write( "t2 = hose 2 time<BR>\n" );
document.write( "g = number of gallons<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "r1*t1 = g<BR>\n" );
document.write( "t1 = 4<BR>\n" );
document.write( "4*t1 = g<BR>\n" );
document.write( "t1 = g/4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "r2*t2 = g<BR>\n" );
document.write( "r2 = g/t2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "(r1+r2)*(t2-2) = g<BR>\n" );
document.write( "substitute g/4 for r1 and g/t2 for r2 to get:<BR>\n" );
document.write( "(g/4 + g/t2) * (t2-2) = g<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "divide both sides of equation by g to get:<BR>\n" );
document.write( "(1/4 + 1/t2) * (t2-2) = 1<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides of the equation by 4*t2 to get:<BR>\n" );
document.write( "(t2 + 4) * (t2 - 2) = 4*t2<BR>\n" );
document.write( "multiply factors out to get:<BR>\n" );
document.write( "(t2)^2 + 4*t2 - 2*t2 - 8 = 4*t2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "subtract 4*t2 from both sides of the equation and combine like terms to get:<BR>\n" );
document.write( "(t2)^2 - 2*t2 - 8 = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "factor this to get:<BR>\n" );
document.write( "(t2 - 4) * (t2 + 2) = 0<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "t2 = 4 OR t2 = -2<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since t2 can't be negative, only good solution would be:<BR>\n" );
document.write( "t2 = 4<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Answer is it takes pipe 2 4 hours to fill the tank.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let g be any number of gallons.<BR>\n" );
document.write( "suppose 100 gallons<BR>\n" );
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document.write( "4r1 = 100<BR>\n" );
document.write( "r1 = 25<BR>\n" );
document.write( "4r2 = 100<BR>\n" );
document.write( "r2 = 25<BR>\n" );
document.write( "working together we get:<BR>\n" );
document.write( "(r1+r2)*2 = 100<BR>\n" );
document.write( "(50)*2 = 100<BR>\n" );
document.write( "100 = 100<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "checks out ok.<BR>\n" );
document.write( "hose 1 takes 4 hours<BR>\n" );
document.write( "hose 2 takes 4 hours<BR>\n" );
document.write( "working together they take 2 hours<BR>\n" );
document.write( "-----\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );