document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356738>Question 356738</A>: <I><SPAN STYLE=\"word-break: break-all;\"> can anyone solve this problem? thank you for that someone.The circumference of a hind wheel of a wagon is 8 decimeters longer than that of the front wheel. In traveling one kilometer, the front wheel makes 62 ½ more revolutions than the hind wheel. Find the circumference of each wheel. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254699 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=254699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It took a few tries because my mathematics was sloppy, even with a calculator, but I think I found the solution.\r<BR>\n" );
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document.write( "Here's how:\r<BR>\n" );
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document.write( "The main equation to work with is c*x = d\r<BR>\n" );
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document.write( "d = distance<BR>\n" );
document.write( "c = circumference<BR>\n" );
document.write( "x = number of revolutions\r<BR>\n" );
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document.write( "First thing you want to do is convert everything to a common measure.\r<BR>\n" );
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document.write( "I used meters.\r<BR>\n" );
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document.write( "1 kilometer = 1000 meters<BR>\n" );
document.write( "8 decimeters = .8 meters\r<BR>\n" );
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document.write( "your formulas to work with are:\r<BR>\n" );
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document.write( "h * x = 1000\r<BR>\n" );
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document.write( "h is the circumference of the hind wheel.\r<BR>\n" );
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document.write( "f * (x + 62.5) = 1000\r<BR>\n" );
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document.write( "f is the circumference of the front wheel.\r<BR>\n" );
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document.write( "since they are both equal to 1000, then they are both equal to each other and you get:\r<BR>\n" );
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document.write( "h * x = f * (x + 62.5)\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "h * x = (f * x) + (62.5 * f)\r<BR>\n" );
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document.write( "you are given that h = f + .8 so you can substitute in this equation to get:\r<BR>\n" );
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document.write( "(f + .8) * x = (f * x) + (62.5 * f)\r<BR>\n" );
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document.write( "remove parentheses in the first equation to get:\r<BR>\n" );
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document.write( "(f * x) + (.8 * x) = (f * x) + (62.5 * f)\r<BR>\n" );
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document.write( "subtract (f * x) from both sides of the equation to get:\r<BR>\n" );
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document.write( ".8 * x = 62.5 * f\r<BR>\n" );
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document.write( "divide both sides of the equation by .8 to get:\r<BR>\n" );
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document.write( "x = 62.5 * f / .8 which becomes:\r<BR>\n" );
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document.write( "x = 78.125 * f\r<BR>\n" );
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document.write( "substitute for x in the equation of f * (x + 62.5) = 1000 to get:\r<BR>\n" );
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document.write( "f * ( 78.125 * f + 62.5) = 1000\r<BR>\n" );
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document.write( "simplify by removing parentheses to get:\r<BR>\n" );
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document.write( "78.125 * f^2 + 62.5 * f = 1000\r<BR>\n" );
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document.write( "subtract 1000 from both sides of the equation to get:\r<BR>\n" );
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document.write( "78.125 * f^2 + 62.5 * f - 1000 = 0\r<BR>\n" );
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document.write( "since this is the standard form of a quadratic equation, we get:\r<BR>\n" );
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document.write( "a = 78.125<BR>\n" );
document.write( "b = 62.5<BR>\n" );
document.write( "c = -1000\r<BR>\n" );
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document.write( "from this, we get:\r<BR>\n" );
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document.write( "2a = 156.25<BR>\n" );
document.write( "-b = -62.5<BR>\n" );
document.write( "b^2 = 3906.25<BR>\n" );
document.write( "4ac = -312500<BR>\n" );
document.write( "b^2 - 4ac = 3906.25 - (-312500) = 316406.25<BR>\n" );
document.write( "sqrt(b^2-4ac) = sqrt(316406.25) = 562.5\r<BR>\n" );
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document.write( "f will be equal to  ( -b +/- sqrt(b^2-4ac) ) / (2a) \r<BR>\n" );
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document.write( "this becomes f = (-62.5 +/- 562.5 ) / 156.25\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "f = 3.2 or f = -4\r<BR>\n" );
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document.write( "since f can't be negative, f must be equal to 3.2.\r<BR>\n" );
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document.write( "since h = f + .8, h must be equal to 4.\r<BR>\n" );
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document.write( "h * x = 1000 becomes 4 * x = 1000 which yields x = 1000 / 4 = 250\r<BR>\n" );
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document.write( "Let y = the number of revolutions of the smaller wheel.\r<BR>\n" );
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document.write( "You get f * y = 1000 which becomes 3.2 * y = 1000 which becomes y = 1000 / 3.2 = 312.5\r<BR>\n" );
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document.write( "y minus x yields 312.5 - 250 which equals 62.5.\r<BR>\n" );
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document.write( "y is equal to x + 62.5 which confirms the solution is good.\r<BR>\n" );
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document.write( "your equations are:\r<BR>\n" );
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document.write( "h * x = 1000 which becomes 4 * 250 = 1000 which becomes 1000 = 1000 which is true.\r<BR>\n" );
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document.write( "f * (x + 62.5) = 1000 which becomes 3.2 * (250 + 62.5) = 1000 which becomes 3.2 * 312.5 = 1000 which becomes 1000 = 1000 which is also true.\r<BR>\n" );
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document.write( "that's your answer.\r<BR>\n" );
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document.write( "the circumference of the front wheel is 3.2 meters.\r<BR>\n" );
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document.write( "the circumference of the hind wheel is 4 meters.\r<BR>\n" );
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document.write( "the number of revolutions of the front wheel is 312.\r<BR>\n" );
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document.write( "the number of revolutions of the hind wheel is 250.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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