document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1093879>Question 1093879</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Estabon poured himself a hot beverage that had a temperature of 203<BR>\n" );
document.write( "degreesF then set it on the kitchen table to cool. The temperature of the kitchen was a constant 68degreesF. If the drink cooled to 182degreesF in 3 minutes, how long will it take for the drink to cool to 104 degrees&#8203;F?\r<BR>\n" );
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document.write( "&#8203;(Do not round until the final answer. Then round to the nearest minute as&#8203; needed.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #708529 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=708529\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> assuming that the cooling of the drink is linear, then you get:\r<BR>\n" );
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document.write( "(203 - 182)/3 = 21/3 = 7 degrees of cooling per minute.\r<BR>\n" );
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document.write( "that's the slope of a linear equation of y = mx + b.\r<BR>\n" );
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document.write( "m is the slope.<BR>\n" );
document.write( "b is the y-intercept, otherwise known as the value of y when x = 0.\r<BR>\n" );
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document.write( "so your equation is y = mx + b which becomes y = -7x + b because the slope is going down because the temperature is dropping at a constant rate of 7 degrees per minute.\r<BR>\n" );
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document.write( "your coordinate points in this equation are (3,182).\r<BR>\n" );
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document.write( "those are the points that you know.\r<BR>\n" );
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document.write( "another point is (0,203).\r<BR>\n" );
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document.write( "(0,203) tells you that when x = 0, y = 203.<BR>\n" );
document.write( "x is the time in minutes.<BR>\n" );
document.write( "y is the temperature.\r<BR>\n" );
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document.write( "(3,182) tells you that when x = 3, y = 182.\r<BR>\n" );
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document.write( "you already know the y-intercept because you know the value of y when x is equal to 0.\r<BR>\n" );
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document.write( "it's 203, but we'll solve for it anyway and we should get that value.\r<BR>\n" );
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document.write( "we'll use the point (3,182).\r<BR>\n" );
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document.write( "the equation is y = -7x + b<BR>\n" );
document.write( "replace y with 182 and x with 3 and we get 182 = -7*3 + b.<BR>\n" );
document.write( "simplify to get 182 = -21 + b.<BR>\n" );
document.write( "add 21 to both sides of the equation to get 203 = b<BR>\n" );
document.write( "that's our y-intercept.\r<BR>\n" );
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document.write( "the equation is therefore y = -7x + 203.\r<BR>\n" );
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document.write( "we want to know how long it will take for the temperature to reach 104.\r<BR>\n" );
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document.write( "since y is the temperature, then we get 104 = -7x + 203.<BR>\n" );
document.write( "subtract 203 from both sides of the equation to get -99 = -7x.<BR>\n" );
document.write( "divide both sides of the equation by -7 to get -99/-7 = x<BR>\n" );
document.write( "solve for x to get x = -99/-7 = 14.14285714 minutes.\r<BR>\n" );
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document.write( "it takes the liquid 14.14285714 minutes to go from 203 degrees to 104 degrees.<BR>\n" );
document.write( "it takes the liquid 3 minutes to go from 203 to 182 degrees.<BR>\n" );
document.write( "it therefore takes the liquid 14.14285714 - 3 = 11.14285714 minute to go from 182 to 104 degrees.\r<BR>\n" );
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document.write( "round to the nearest minutes to get 3 minutes from 203 to 182 and 11 minutes from 182 to 104 for a total of 14 minutes.\r<BR>\n" );
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document.write( "we solved this using linear algebra, but we could have solved just using logic.\r<BR>\n" );
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document.write( "203 - 182 = 21 divided by 3 = 7 degrees of loss per minute.\r<BR>\n" );
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document.write( "182 - 104 = 78 / 7 = 11.14285714 minutes to go from 182 to 104.\r<BR>\n" );
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document.write( "total time from 203 to 104 is 11.14285714 + 3 = 14.14285714 minutes.\r<BR>\n" );
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document.write( "we can graph this equation and it will show us where the critical points are.\r<BR>\n" );
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document.write( "here's the graph.\r<BR>\n" );
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