document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=507307>Question 507307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A water tank is being emptied so that the height y (in feet) of the water inside the tank decreases at a linear rate with time t measured in hours past 12 noon. If the height was 15ft at 1pm and 7.5ft at 6pm, find\r<BR>\n" );
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document.write( "(a)the equation relating y to t<BR>\n" );
document.write( "(b)the height at 12 noon<BR>\n" );
document.write( "(c)the total time required to empty the tank </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #340434 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><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=340434\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A water tank is being emptied so that the height y (in feet) of the water inside the tank decreases at a linear rate with time t measured in hours past 12 noon. If the height was 15ft at 1pm and 7.5ft at 6pm, find <BR>\n" );
document.write( "(a)the equation relating y to t<BR>\n" );
document.write( "(b)the height at 12 noon<BR>\n" );
document.write( "(c)the total time required to empty the tank<BR>\n" );
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document.write( "Since there is a straight line relationship between height of water and time (hours), you can use standard form of equation for a straight line which is: y=mx+b, m=slope, b=intercept<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Between 1 and 6 pm, a period of 5 hours, the height dropped from 15 ft to 7.5 ft, which gives a slope of (15-7.5)/(1-6)=7.5/-5=-1.5ft/hr=m. You now have part of the equation completed, y=-1.5x+b. To find b, use one of the given points on the line,(1,15). <BR>\n" );
document.write( "15=-1.5*1+b<BR>\n" );
document.write( "15=-1.5+b<BR>\n" );
document.write( "b=16.5<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "y=-1.5x+16.5<BR>\n" );
document.write( "ans:<BR>\n" );
document.write( "(a)the equation relating y to t: f(t)=-1.5t+16.5<BR>\n" );
document.write( "(b)the height at 12 noon: f(0)=-1.5*0+16.5=16.5ft<BR>\n" );
document.write( "(c)the total time required to empty the tank:<BR>\n" );
document.write( "set y=0, then solve for t<BR>\n" );
document.write( "0=-1.5t+16.5<BR>\n" );
document.write( "1.5x=16.5<BR>\n" );
document.write( "t=11hrs<BR>\n" );
document.write( "see graph below as a visual check on answers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+300%2C+-10%2C+20%2C+-10%2C+20%2C-1.5x%2B16.5%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+300%2C+-10%2C+20%2C+-10%2C+20%2C-1.5x%2B16.5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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