document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084499>Question 1084499</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the diameter of a hose is inversely proportional to the time it takes to fill a tank.<BR>\n" );
document.write( "if the diameter of hose is 1 inch, and the filling rate is 10 ft per second, how much water will be in the tank after 1.75 seconds? \r<BR>\n" );
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document.write( "appreciate your help,\r<BR>\n" );
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document.write( "Gul </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698598 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=698598\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the diameter of the hose is inversely proportional to the time it takes to fill the tank.\r<BR>\n" );
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document.write( "this means that when the diameter of the hose is larger, it takes less time to fill the tank.\r<BR>\n" );
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document.write( "the formula for indirect variation is y = k/x\r<BR>\n" );
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document.write( "k is the constant of variation.\r<BR>\n" );
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document.write( "it always stays the same once it is set up initially based on the problem statement.\r<BR>\n" );
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document.write( "you are given that it takes 1.75 seconds to fill the tank when the diameter of the hose is 1 inch.\r<BR>\n" );
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document.write( "the formula of y = k/x becomes 1.75 = k/1\r<BR>\n" );
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document.write( "solve for k to get k = 1.75\r<BR>\n" );
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document.write( "that's the constant of variation.\r<BR>\n" );
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document.write( "when the diameter of the hose is 2 inches, it should take half the time to fill the tank, and it does:\r<BR>\n" );
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document.write( "y = k/x becomes y = 1.75/2 = .875 seconds.\r<BR>\n" );
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document.write( "the diameter of the hose is doubled and it takes half the time to fill the tank.\r<BR>\n" );
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document.write( "how does this relate to the rate at which the hose is delivering water?\r<BR>\n" );
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document.write( "the problem states that the 1 inch hose delivers 10 cubic feet of water per second.\r<BR>\n" );
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document.write( "rate * time = quantity\r<BR>\n" );
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document.write( "the 1 inch hose delivers water at the rate of 10 cubic feet per second for 1.75 seconds, so the formula becomes:\r<BR>\n" );
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document.write( "10 cubic feet per second * 1.75 seconds = 17.5 cubic feet of water.\r<BR>\n" );
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document.write( "if the tank is full, then the capacity of the tank has to be 17.5 cubic feet of water.\r<BR>\n" );
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document.write( "the 1 inch hose delivers 17.5 cubic feet of water in 1.75 seconds.\r<BR>\n" );
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document.write( "note that i used cubic feet instead of feet because we're talking volume of water and volume is measured in cubic units.\r<BR>\n" );
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document.write( "now, our indirect ratio says that the time it takes is indirectly proportional to the diameter of the hose, and we figured out that the constant of variation was 1.75.\r<BR>\n" );
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document.write( "when the diameter of the hose was 1 inch, it took 1.75 seconds to fill the tank.\r<BR>\n" );
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document.write( "when the diameter of the hose was 2 inches, the formula said that y = 1.75 / 2 and we got that it would then take .875 seconds to fill the tank.\r<BR>\n" );
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document.write( "the rate * time = quantity formula that was 10 * 1.75 = 17.5 now becomes:\r<BR>\n" );
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document.write( "x * .875 = 17.5\r<BR>\n" );
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document.write( "x is the rate.<BR>\n" );
document.write( ".875 is the time<BR>\n" );
document.write( "17.5 is the cubic feet of water that is the capacity of the tank.\r<BR>\n" );
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document.write( "solve for x to get x = 17.5 / .875 = 20\r<BR>\n" );
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document.write( "when the diameter of the hose is 2 inches, it is delivering 20 cubic feet of water in one second.\r<BR>\n" );
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document.write( "the diameter of the hose was doubled and the time it took to fill the tank became half and the rate that the hose delivered the water was doubled.\r<BR>\n" );
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document.write( "makes sense to me.\r<BR>\n" );
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document.write( "hopefully it will make sense to you.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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