document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=323282>Question 323282</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A large pump can fill a 10,000 gallon tank 5 hours faster than a small pump. The large pump outputs water 100 gallons per hour faster than the small pump. Find the number of gallons pumped in 1 hour by each pump. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #231410 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=231410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A large pump can fill a 10,000 gallon tank 5 hours faster than a small pump.<BR>\n" );
document.write( " The large pump outputs water 100 gallons per hour faster than the small pump.<BR>\n" );
document.write( " Find the number of gallons pumped in 1 hour by each pump.<BR>\n" );
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document.write( "Let x = gal/hr of the smaller pump<BR>\n" );
document.write( "(x+100) = gal/hr of the larger pump<BR>\n" );
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document.write( "small pump time - large pump time = 5 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2Fx ALIGN=MIDDLE  ALT=\"10000%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2F%28x%2B100%29 ALIGN=MIDDLE  ALT=\"10000%2F%28x%2B100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5 <BR>\n" );
document.write( "multiply by x(x+100), results<BR>\n" );
document.write( "10000(x+100) - 10000x = 5x(x+100)<BR>\n" );
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document.write( "10000x + 1000000 - 10000x = 5x^2 + 500x<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "0 = 5x^2 + 500x - 1000000 <BR>\n" );
document.write( "Simplify, divide by 5<BR>\n" );
document.write( "x^2 + 100x - 200000 = 0<BR>\n" );
document.write( "Factors<BR>\n" );
document.write( "(x + 500)(x - 400) = 0<BR>\n" );
document.write( "x = 400 gal/hr, the rate of the small pump<BR>\n" );
document.write( "and<BR>\n" );
document.write( "400 + 100 = 500 gal/hr, the rate of the large pump<BR>\n" );
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document.write( "Check solution, find the time of each pump<BR>\n" );
document.write( "10000/400 = 25 hrs<BR>\n" );
document.write( "10000/500 = 20 hrs<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "difference: 5 hrs </SPAN>\n" );
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