document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191661>Question 1191661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi<BR>\n" );
document.write( "A pool 100cm by 100cm  by 435cm is to be filled to the brim. Water from A and B flows at the rate of 150 litres per minute and 250 litres per  minute respectively. If A was turned on 3 minutes after  B is turned on how long will it take to fill the pool.\r<BR>\n" );
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document.write( "Thanks<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823467 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = duration (in minutes) that hose B is running<BR>\n" );
document.write( "x-3 = duration (in minutes) that hose A is running<BR>\n" );
document.write( "This is because hose B had a 3 minute head start, so it runs for 3 minutes longer.\r<BR>\n" );
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document.write( "Based on that and the given speeds, we can say,<BR>\n" );
document.write( "A = 150(x-3) = 150x-450 = amount of water hose A contributes<BR>\n" );
document.write( "B = 250x = amount of water hose B contributes<BR>\n" );
document.write( "Amounts are in liters.\r<BR>\n" );
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document.write( "A+B = (150x-450)+250x = 400x-450 = total amount of water from both hoses after x minutes elapse.\r<BR>\n" );
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document.write( "At this point, we need to find out how much water will fill the pool. We'll need the volume of the pool.\r<BR>\n" );
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document.write( "Assuming the pool is a rectangular prism, then,<BR>\n" );
document.write( "Volume = (length)*(width)*(height)<BR>\n" );
document.write( "V = L*W*H<BR>\n" );
document.write( "V = (100 cm)*(100 cm)*(435 cm)<BR>\n" );
document.write( "V = (100*100*435)*(cm*cm*cm)<BR>\n" );
document.write( "V = 4,350,000 cm^3<BR>\n" );
document.write( "Think of tiny 1 cm by 1 cm by 1 cm blocks. <BR>\n" );
document.write( "We'll need 4,350,000 of them (a little over 4.3 million) to fill the pool if we stack and pack the blocks in perfectly.\r<BR>\n" );
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document.write( "Side note: cm^3 = cubic centimeter = cubic cm = cc\r<BR>\n" );
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document.write( "By definition, 1 cm^3 is equal to 1 mL<BR>\n" );
document.write( "The pool has a volume of 4,350,000 mL<BR>\n" );
document.write( "To convert to liters, we divide by 1000 since 1000 mL = 1 liter\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "(4,350,000)/1000 = 4,350<BR>\n" );
document.write( "Just chop off the last 3 zeros of \"4,350,000\" to arrive at 4,350\r<BR>\n" );
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document.write( "The pool has a volume of 4,350 liters. \r<BR>\n" );
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document.write( "Set this equal to the A+B expression mentioned earlier and solve for x.<BR>\n" );
document.write( "400x-450 = 4350<BR>\n" );
document.write( "400x = 4350+450<BR>\n" );
document.write( "400x = 4800<BR>\n" );
document.write( "x = 4800/400<BR>\n" );
document.write( "x = <font color=red>12</font><BR>\n" );
document.write( "It will take <font color=red>12 minutes</font> from the time hose B (ie the first hose) is activated, to completely fill the pool with both hoses based on the conditions stated in the instructions.\r<BR>\n" );
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document.write( "Since hose B contributes water at a rate of 250 liters/min, and does so for 12 minutes, it contributes 250*12 = 3000 liters of water.\r<BR>\n" );
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document.write( "Hose A starts 3 minutes later and has a duration of x-3 = 12-3 = 9 minutes. It contributes 150*9 = 1350 liters.\r<BR>\n" );
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document.write( "The two hoses combine to give A+B = 1350+3000 = 4350 liters which is the volume of the pool (again assuming it is a rectangular prism). <BR>\n" );
document.write( "Another assumption is that none of the water spills out of the pool, and evaporation shouldn't be that big an issue.\r<BR>\n" );
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document.write( "Answer: <font color=red>12 minutes</font><BR>\n" );
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