document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1177723>Question 1177723</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It takes pump A 2 hours less time than pump B to empty a pool. Pump A is started at 8:00am and pump B at 10:00am. At 12:00pm 60% of the pool.is empty when pump B broke down. How much time after 12:00pm would it take pump A to empty the pool? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #806841 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=806841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rate * time = quantity\r<BR>\n" );
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document.write( "let quantity = 1 empty pool.<BR>\n" );
document.write( "let t equal the time it takes pump B to empty the pool.<BR>\n" );
document.write( "let t-2 equal the time it takes pump A to empty the pool.<BR>\n" );
document.write( "let a equal the rate that pump A empties the pool.<BR>\n" );
document.write( "let b equal the rate that pump B empties the pool.\r<BR>\n" );
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document.write( "your equations are:<BR>\n" );
document.write( "a * (t-2) = 1 for pump A.<BR>\n" );
document.write( "b * t = 1 for pump B.\r<BR>\n" );
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document.write( "solve for a in the first equation to get a = 1/(t-2).<BR>\n" );
document.write( "solve for b in the second equation to get b = 1/t.\r<BR>\n" );
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document.write( "pump A starts at 8:00 am and pump B starts at 10:00 am.<BR>\n" );
document.write( "at 12:00 pm, they have emptied 60% of the pool.<BR>\n" );
document.write( "pump B breaks down at 12:00 pm.<BR>\n" );
document.write( "pump A worked from 8:00 am to 12:00 pm.<BR>\n" );
document.write( "pump B worked from 10:00 am to 12:00 pm.<BR>\n" );
document.write( "pump A worked for 4 hours.<BR>\n" );
document.write( "pump B worked for 2 hours.\r<BR>\n" );
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document.write( "when pump A worked for 4 hours and pump B worked for 2 hours, they emptied 60% of the pool.\r<BR>\n" );
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document.write( "the equation for that is 4*a + 2*b = .6.\r<BR>\n" );
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document.write( "since a = 1/(t-2) and b = 1/t, replace a and b in the equation with their equivalent expressions in terms of t to get 4/(t-2) + 2/t = .6\r<BR>\n" );
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document.write( "multiply both sides of this equation by t(t-2) to get 4t + 2(t-2) = .6t(t-2)\r<BR>\n" );
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document.write( "simplify to get 4t + 2t - 4 = .6t^2 - 1.2t.\r<BR>\n" );
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document.write( "combine like terms to get 6t - 4 = .6t^2 - 1.2t.\r<BR>\n" );
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document.write( "subtract 6t from both sides of the equation and add 4 to both sides of the equation to get 0 = .6t^2 - 1.2t - 6t + 4.\r<BR>\n" );
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document.write( "combine like terms to get 0 = .6t^2 - 7.2t + 4\r<BR>\n" );
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document.write( "factor this quadratic equation to get t = 11.416025603091 or t = 0.58397439690936.\r<BR>\n" );
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document.write( "t = 0.58397439690936 won't work because then t - 2 would be negative.\r<BR>\n" );
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document.write( "you get t = 11.416025603091.\r<BR>\n" );
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document.write( "since a = 1/(t-2), then a = .1062019202.\r<BR>\n" );
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document.write( "since b = 1/t, then b = .0875961595.\r<BR>\n" );
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document.write( "to confirm a and b values are good, replace a and b in the equation of 4a + 2b = .6 to get .6 = .6, which is true, confirming the values are good.\r<BR>\n" );
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document.write( "you now have:\r<BR>\n" );
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document.write( "t = 11.416025603091<BR>\n" );
document.write( "a = .1062019202<BR>\n" );
document.write( "b = .0875961595\r<BR>\n" );
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document.write( "since .6 of the pool has been filled, then .4 of the pool remains to be filled by pump A.\r<BR>\n" );
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document.write( "let r = the time for pump A to fill .4 of the pool.<BR>\n" );
document.write( "you get a * r = .4<BR>\n" );
document.write( "solve for r to get r = .4/a<BR>\n" );
document.write( "this becomes r = .4/.1062019202<BR>\n" );
document.write( "solve for r to get r = 3.766410241 hours.\r<BR>\n" );
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document.write( "you have the final result for filling the pool as><BR>\n" );
document.write( "4 hours for pump A plus 2 hours for pump B plus another 3.766410241 hours for pump A to fill the pool.<BR>\n" );
document.write( "this results in 7.766410241 for pump A and 2 hours for pump B to fill the pool.<BR>\n" );
document.write( "since pump A works at a rate of .1062019202 of the pool in 1 hour and pump B works at a rate of .0875961595 of the pool in 1 hour, then:<BR>\n" );
document.write( "7.766410241 * .1062019202 + 2 * .0875961595 = 1<BR>\n" );
document.write( "this confirms the calculations are correct.\r<BR>\n" );
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document.write( "your answer is that it would take pump A 3.766410241 hours to finish pumping the pool after pump B broke down.\r<BR>\n" );
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document.write( "that is if my assumptions and calculations are correct.<BR>\n" );
document.write( "i think that they are, so i'll go with this answer until i'm proven wrong.<BR>\n" );
document.write( "let me know if you're good with this answer, or if another answer was expected.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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