document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1057921>Question 1057921</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me.\r<BR>\n" );
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document.write( "A company buys a new pump that can pump 10.0 gal./min faster than its old one. It can fill the company's 500.0 gallon tank 15.0 minutes faster than the old pump. What was the speed of the old pump?\r<BR>\n" );
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document.write( "Round to three significant digits. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #672924 by </B><A HREF=/tutors/aboutme.mpl?userid=LinnW><B>LinnW(1048)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=LinnW><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=LinnW><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=672924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set s = speed in gals per minute of the old pump<BR>\n" );
document.write( "(s+10) = speed of the new pump<BR>\n" );
document.write( "Set t = time to fill the tank with the old pump<BR>\n" );
document.write( "s*t = 500, that is at the speed of the old pump times old time = 500 gallons pumped.<BR>\n" );
document.write( "(s+10)(t-15) = 500<BR>\n" );
document.write( "that is the new pump speed times a time of 15 minutes less fills the 500 gallons<BR>\n" );
document.write( "Since s*t = 500, if we divide each side by s we get t = (500/s)<BR>\n" );
document.write( "Substitute (500/s) for t in (s+10)(t-15) = 500<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28s%2B10%29%28%28500%2Fs%29-15%29+=+500 ALIGN=MIDDLE  ALT=\"%28s%2B10%29%28%28500%2Fs%29-15%29+=+500\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%28500%2Fs%29-15s%2B10%28500%2Fs%29-150+=+500+ ALIGN=MIDDLE  ALT=\"s%28500%2Fs%29-15s%2B10%28500%2Fs%29-150+=+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=500-15s%2B%285000%2Fs%29-150+=+500+ ALIGN=MIDDLE  ALT=\"500-15s%2B%285000%2Fs%29-150+=+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=350-15s%2B%285000%2Fs%29+=+500+ ALIGN=MIDDLE  ALT=\"350-15s%2B%285000%2Fs%29+=+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add -350 to each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=350-15s%2B%285000%2Fs%29+=+500+ ALIGN=MIDDLE  ALT=\"350-15s%2B%285000%2Fs%29+=+500+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15s%2B%285000%2Fs%29+=+150+ ALIGN=MIDDLE  ALT=\"-15s%2B%285000%2Fs%29+=+150+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply each side by s<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15s%5E2%2B5000+=+150s+ ALIGN=MIDDLE  ALT=\"-15s%5E2%2B5000+=+150s+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "add -150s to each side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15s%5E2-150s%2B5000+=+0+ ALIGN=MIDDLE  ALT=\"-15s%5E2-150s%2B5000+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide each side by -5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3s%5E2%2B30s-1000+=+0+ ALIGN=MIDDLE  ALT=\"3s%5E2%2B30s-1000+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using a quadratic solver we have two roots<BR>\n" );
document.write( "approximately 13.93 and -23.93<BR>\n" );
document.write( "Since the pump speed must be positive, the original<BR>\n" );
document.write( "pump speed is 13.93 gallons per minute.<BR>\n" );
document.write( "Notice that since s*t = 500, (13.93)(t) = 500<BR>\n" );
document.write( "t = 500/13.93<BR>\n" );
document.write( "t = 35.893<BR>\n" );
document.write( "Let's verify that (s+10)(t-15) = 500 works<BR>\n" );
document.write( "(13.93+10)(35.893-15) ?= 500<BR>\n" );
document.write( "(23.93)(20.893) = 499.96949<BR>\n" );
document.write( "So we must be on track </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );