document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=207761>Question 207761</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have received the solution that you sent to me..thanks a lot. but i need again your help..ive been trying to solve this a lot of times but it seems that my knowledge is not yet enough...can you help me solve these two problems??<BR>\n" );
document.write( "1)A water tank is supplied by pipes A and B and emptied by pipe C. If the pipes are open, the tank can be filled in 15 hours. If the tank is full and pipes A and C are open, the tank can be emptied in 10 hours. If the tank is full and pipes B and C are open, the tank can be emptied in 6 hours. If pipe A supplies 50 more liters a minute than pipe B and the capacity of the tank is 45 000 liters, find the number of liters that pass through each pipe per minute.\r<BR>\n" );
document.write( "\n" );
document.write( "2)A contractor worked for 7 days after which he sought the help of his son and together they finished a painting job in 5 days. Had he sought the help of his son 3 days after he started working, they would have finished the job in 7 days. How long would it take each to finish the job alone?\r<BR>\n" );
document.write( "\n" );
document.write( "Im hoping for an immediate response, thanks a lot.godbless </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #157259 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=157259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)A water tank is supplied by pipes A and B and emptied by pipe C. <BR>\n" );
document.write( "If the pipes are open, the tank can be filled in 15 hours. <BR>\n" );
document.write( "If the tank is full and pipes A and C are open, the tank can be emptied in 10 hours. <BR>\n" );
document.write( "If the tank is full and pipes B and C are open, the tank can be emptied in 6 hours. <BR>\n" );
document.write( "If pipe A supplies 50 more liters a minute than pipe B and the capacity of the<BR>\n" );
document.write( " tank is 45 000 liters, find the number of liters that pass through each pipe per minute.<BR>\n" );
document.write( "Let A, B, C = the capacities of the three pipes (in liters per hour)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write an equation for each statement:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"If the pipes are open, the tank can be filled in 15 hours. <BR>\n" );
document.write( "Eq1: 15A + 15B - 15C = 45000 (full is plus)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"tank is full and pipes A and C are open, the tank can be emptied in 10 hrs.\" <BR>\n" );
document.write( "Eq2: 10A - 10C = -45000 (emptied is minus)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"tank is full and pipes B and C are open, the tank can be emptied in 6 hrs\"<BR>\n" );
document.write( "Eq3: 6B - 6C = -45000<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"pipe A supplies 50 more liters a minute than pipe B \"<BR>\n" );
document.write( "Eq4: A = B + 60(50)<BR>\n" );
document.write( "A = B + 3000; converted to liters per hr<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using eq1 and 4, substitute (B+3000) for A<BR>\n" );
document.write( "15(B+3000) + 15B - 15C = 45000<BR>\n" );
document.write( "15B + 45000 + 15B - 15C = 45000<BR>\n" );
document.write( "30B - 15C = 45000 - 45000<BR>\n" );
document.write( "30B - 15C = 0<BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "30B = 15C<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "2B = C<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Using eq3: <BR>\n" );
document.write( "6B - 6C = -45000<BR>\n" );
document.write( "Simplify, divide by 6<BR>\n" );
document.write( "B - C = -7500<BR>\n" );
document.write( "substitute 2B for C<BR>\n" );
document.write( "B - 2B = -7500<BR>\n" );
document.write( "-B = -7500<BR>\n" );
document.write( "B = 7500 liters/min, B pipe<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "2B = C<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "2(7500) = C<BR>\n" );
document.write( "C = 15000 liters/min, C pipe<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find A using eq4<BR>\n" );
document.write( "A = B + 3000<BR>\n" );
document.write( "A = 7500 + 3000<BR>\n" );
document.write( "A = 10500 liters/min, A pipe<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solutions in eq1, using a calc:<BR>\n" );
document.write( "15(10500) + 15(7500) - 15(15000) = 45000<BR>\n" );
document.write( ";<BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "\n" );
document.write( "2)A contractor worked for 7 days after which he sought the help of his son and<BR>\n" );
document.write( " together they finished a painting job in 5 days. Had he sought the help of his<BR>\n" );
document.write( " son 3 days  after he started working, they would have finished the job in 7 days.<BR>\n" );
document.write( " How long would it take each to finish the job alone?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = time for Dad alone<BR>\n" );
document.write( "Let y = time for son alone<BR>\n" );
document.write( "Let the completed job = 1<BR>\n" );
document.write( ":<BR>\n" );
document.write( "write an equation for each scenario.<BR>\n" );
document.write( ":<BR>\n" );
document.write( " 1st scenario Dad works a total of 12 days<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fx ALIGN=MIDDLE  ALT=\"12%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fy ALIGN=MIDDLE  ALT=\"5%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by xy, results<BR>\n" );
document.write( "12y + 5x = xy<BR>\n" );
document.write( ":<BR>\n" );
document.write( "2nd scenario Dad works a total of 10 days<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2Fx ALIGN=MIDDLE  ALT=\"10%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7%2Fy ALIGN=MIDDLE  ALT=\"7%2Fy\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by xy, results<BR>\n" );
document.write( "10y + 7x = xy<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Therefore<BR>\n" );
document.write( "12y + 5x = 10y + 7x<BR>\n" );
document.write( "12y - 10y = 7x - 5x<BR>\n" );
document.write( "2y = 2x<BR>\n" );
document.write( "y = x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "This greatly simplifies things, using the first equation, replace y with x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Fx ALIGN=MIDDLE  ALT=\"12%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Fx ALIGN=MIDDLE  ALT=\"5%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "Multiply by x<BR>\n" );
document.write( "12 + 5 = x<BR>\n" );
document.write( "x = 17 days, Dad working alone<BR>\n" );
document.write( "and<BR>\n" );
document.write( "y = 17 days, son working alone<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Checks out in the 2nd equation<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );