document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=58489>Question 58489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hello i just wanted to check to see if I was doing this word problem correctly. The word problem says...\r<BR>\n" );
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document.write( "A tank can be filled by an inlet pipe in 8 hours when the drain pipe is open and in 5 hours if the drain pipe is closed. How long will it take to empty a full tank when the inlet pipe is closed.\r<BR>\n" );
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document.write( "i did...\r<BR>\n" );
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document.write( "X/8 (x over eight) + X/5 (x over five) = 1\r<BR>\n" );
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document.write( "40 [X/8 + X/5 = 1]\r<BR>\n" );
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document.write( "then got...\r<BR>\n" );
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document.write( "5x + 8x = 40\r<BR>\n" );
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document.write( "13x= 40\r<BR>\n" );
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document.write( "x= 3 1/3\r<BR>\n" );
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document.write( "if this is correct, wrong, or an easier way to do thi problem it would be very helpful to know. Thank You! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40066 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20054)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=40066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><font size = 4 color = \"darkblue\"><b>\r\n" );
document.write( "A tank can be filled by an inlet pipe in 8 hours when the drain pipe \r\n" );
document.write( "is open and in 5 hours if the drain pipe is closed. How long will it \r\n" );
document.write( "take to empty a full tank when the inlet pipe is closed. \r\n" );
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document.write( "I'm afraid your method is wrong.  Only 3 1/3 hours is much too fast \r\n" );
document.write( "for the drain pipe to be able to empty the pool if it only slows \r\n" );
document.write( "the fill pipe down from filling it in 5 hours to filling it in 8 \r\n" );
document.write( "hours. If it drained that fast, the inlet pipe would never be able \r\n" );
document.write( "to fill the pool at all when the drain pipe was open for it would\r\n" );
document.write( "be draining water out much faster than the inlet pipe was putting \r\n" );
document.write( "water in!\r\n" );
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document.write( "Here's a method very much like distance-rate-time problems that I \r\n" );
document.write( "think you may understand better.\r\n" );
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document.write( "Let's make this DRT-chart, except here the D stands for \"Deeds Done\" \r\n" );
document.write( "rather than \"Distance\".  So D represents the number of deeds, or \r\n" );
document.write( "poolfuls it caused.\r\n" );
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document.write( "                      D             R           T  \r\n" );
document.write( "                    No. of       Rate in    No. of hrs.  \r\n" );
document.write( "                   poolfuls      pool/hr    required\r\n" );
document.write( "Inlet pipe alone                                  \r\n" );
document.write( "Drain pipe alone                                \r\n" );
document.write( "both open                                       \r\n" );
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document.write( "Let x = the length of time required for the drain pipe to empty the\r\n" );
document.write( "pool when the inlet pipe is open.\r\n" );
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document.write( "First fill in the three times, 5 hours for the inlet pipe, x hours\r\n" );
document.write( "for the drain pipe, and 8 hours when they are both open.\r\n" );
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document.write( "                      D             R           T\r\n" );
document.write( "                    No. of       Rate in    No. of hrs.  \r\n" );
document.write( "                   poolfuls      pool/hr    required\r\n" );
document.write( "Inlet pipe alone                               5\r\n" );
document.write( "Drain pipe alone                               x\r\n" );
document.write( "both open                                      8\r\n" );
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document.write( "Next we will fill in the number of poolfuls.\r\n" );
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document.write( "The inlet pipe caused the GAIN of 1 poolful in 5 hours.  So we put\r\n" );
document.write( "1 for the number of poolfuls it caused in the 5 hours it was open\r\n" );
document.write( "by itself.\r\n" );
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document.write( "                      D             R           T\r\n" );
document.write( "                    No. of       Rate in    No. of hrs.  \r\n" );
document.write( "                   poolfuls      pool/hr    required\r\n" );
document.write( "Inlet pipe alone        1                      5\r\n" );
document.write( "Drain pipe alone                               x\r\n" );
document.write( "both open                                      8\r\n" );
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document.write( "Now the drain pipe caused a LOSS of 1 poolful in x hours. So we\r\n" );
document.write( "put -1 for the number of poolfuls it caused in the x hours it was\r\n" );
document.write( "open by itself.  (That -1 is the tricky part!)\r\n" );
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document.write( "                      D             R           T\r\n" );
document.write( "                    No. of       Rate in    No. of hrs.  \r\n" );
document.write( "                   poolfuls      pool/hr    required\r\n" );
document.write( "Inlet pipe alone        1                      5\r\n" );
document.write( "Drain pipe alone       -1                      x\r\n" );
document.write( "both open                                      8\r\n" );
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document.write( "Now when both were open that caused a GAIN of 1 poolful in 8 hours.\r\n" );
document.write( "So we put 1 for the number of poolfuls they caused in the 8 hours \r\n" );
document.write( "they both were open. So we fill in 1 for the no. of poolfuls caused \r\n" );
document.write( "by both of them being open.\r\n" );
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document.write( "                      D             R           T\r\n" );
document.write( "                    No. of       Rate in    No. of hrs.  \r\n" );
document.write( "                   poolfuls      pool/hr    required\r\n" );
document.write( "Inlet pipe alone        1                      5\r\n" );
document.write( "Drain pipe alone       -1                      x\r\n" );
document.write( "both open               1                      8\r\n" );
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document.write( "Now we fill in the rates by using R = D/T.\r\n" );
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document.write( "                      D             R           T\r\n" );
document.write( "                    No. of       Rate in    No. of hrs.  \r\n" );
document.write( "                   poolfuls      pool/hr    required\r\n" );
document.write( "Inlet pipe alone        1          1/5         5\r\n" );
document.write( "Drain pipe alone       -1         -1/x         x\r\n" );
document.write( "both open               1          1/8         8\r\n" );
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document.write( "Now the logic in setting up the equation is just like\r\n" );
document.write( "when a boat is in a river going downstream, we add the\r\n" );
document.write( "rate of the boat in still water and the rate of the \r\n" );
document.write( "stream to get the combined rate.  So we use the same \r\n" );
document.write( "idea here:\r\n" );
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document.write( "Rate of inlet pipe + Rate of drain pipe = their combined rate, or\r\n" );
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document.write( "             1/5   +        (-1/x)      =        1/8\r\n" );
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document.write( "                              1/5 - 1/x = 1/8 \r\n" );
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document.write( "Solve that and you'll get 13 1/3 hours for the drain pipe to \r\n" );
document.write( "drain 1 full pool.  That answer makes a lot more sense.\r\n" );
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document.write( "Edwin</PRE><BR>\n" );
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