document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1023619>Question 1023619</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, basically could somebody show me the steps as to how the word problem below was turned into the equation? I want to know how the quadratic equation was made step by step? The equation is at the bottom after the word problem. Many thanks\r<BR>\n" );
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document.write( "\" TAHIR HAS A REGULAR CYCLE TRAINING ROUTE THAT IS 60KM LONG. IF TAHIR CYCLES 3KMH SLOWER THAN HIS RACING SPEED,IT TAKES HIM 3 HOURS AND 20 MINUTES LONGER TO COMPLETE THE ROUTE.\r<BR>\n" );
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document.write( "A) WORK OUT TAHIR'S RACING SPEED. STATE IN WORDS WHAT ALGEBRAIC METHOD YOU ARE USING AT EACH STAGE.\r<BR>\n" );
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document.write( "B) CHECK YOUR ANSWER BY USING TWO FURTHER ALTERNATIVE METHODS FOR SOLVING QUADRATIC EQUATIONS.\r<BR>\n" );
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document.write( "C) EVALUATE ALL THREE METHODS FOR EFFICIENCY AND EFFECTIVENESS.\r<BR>\n" );
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document.write( "V^2 - 3V - 54 = 0\r<BR>\n" );
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document.write( "TAHIR HAS A REGULAR CYCLE TRAINING ROUTE THAT IS 60KM LONG. IF TAHIR CYCLES 3KMH SLOWER THAN HIS RACING SPEED,IT TAKES HIM 3 HOURS AND 20 MINUTES LONGER TO COMPLETE THE ROUTE.\r<BR>\n" );
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document.write( "A) WORK OUT TAHIR'S RACING SPEED. STATE IN WORDS WHAT ALGEBRAIC METHOD YOU ARE USING AT EACH STAGE.\r<BR>\n" );
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document.write( "B) CHECK YOUR ANSWER BY USING TWO FURTHER ALTERNATIVE METHODS FOR SOLVING QUADRATIC EQUATIONS.\r<BR>\n" );
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document.write( "C) EVALUATE ALL THREE METHODS FOR EFFICIENCY AND EFFECTIVENESS.\"\r<BR>\n" );
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document.write( "V^2 - 3V - 54 = 0    (Please show me how the made that word problem into the equation? I know the answers are V = 9 or -6  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #639149 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=639149\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "if your final equation is v^2 - 9v - 54 = 0, then the factors are (v-9) * (v+6).\r<BR>\n" );
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document.write( "the basic equation is rate * time = distance.\r<BR>\n" );
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document.write( "distance equals 60 km.<BR>\n" );
document.write( "speed = r kmph<BR>\n" );
document.write( "time = t hours.\r<BR>\n" );
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document.write( "the basic equation becomes r * t = 60\r<BR>\n" );
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document.write( "when you are traveling 3 kmph slower, the rate becomes r-3.\r<BR>\n" );
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document.write( "when it takes 3 hours and 20 minutes longer, the time becomes t + 3 and 1/3.\r<BR>\n" );
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document.write( "your rate * time equation becomes (r-3) * (t + 3 + 1/3) = 60.\r<BR>\n" );
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document.write( "the distance is the same.<BR>\n" );
document.write( "the rate is 3kmph slower.<BR>\n" );
document.write( "the time is 3 and 1/3 hours longer.\r<BR>\n" );
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document.write( "you have 2 equations that need to be solved simultaneously.\r<BR>\n" );
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document.write( "they are r * t = 60 and (r-3) * (t + 3.33...) = 60\r<BR>\n" );
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document.write( "from r * t = 60, solve for t to get t = 60 / r.\r<BR>\n" );
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document.write( "in (r-3) * (t + 3.33...) = 60, replace t with 60 / r to get:\r<BR>\n" );
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document.write( "(r-3) * (60/r + 3.33...) = 60\r<BR>\n" );
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document.write( "multiply both sides of the equation by r to get:\r<BR>\n" );
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document.write( "(r-3) * (60 + 3.33... * r) = 60 * r\r<BR>\n" );
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document.write( "multiply the factors to get:\r<BR>\n" );
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document.write( "60r + 3.33... * r^2 - 180 - 10 * r = 60r\r<BR>\n" );
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document.write( "the 60r on the left side of the equation and the 60 r on the right side of the equation cancel out and you get:\r<BR>\n" );
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document.write( "3.33... * r^2 - 180 - 10 * r = 0\r<BR>\n" );
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document.write( "divide both sides of the equation by 3.33... (this is really 3 and 1/3), to get:\r<BR>\n" );
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document.write( "r^2 - 54 - 3r = 0\r<BR>\n" );
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document.write( "re-arrange the terms in descending order of degree to get:\r<BR>\n" );
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document.write( "r^2 - 3r - 54 = 0.\r<BR>\n" );
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document.write( "i used r for rate rather than v for velocity.<BR>\n" );
document.write( "it doesn't matter.<BR>\n" );
document.write( "the answer is the same.\r<BR>\n" );
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document.write( "from r^2 - 3r - 54, you can factor the equation to get:\r<BR>\n" );
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document.write( "(r-9) * (r+6) = 0\r<BR>\n" );
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document.write( "that makes r = 9 or -6.\r<BR>\n" );
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document.write( "r can't be negative, so r = 9.\r<BR>\n" );
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document.write( "when r = 9, r * t = 60 becomes 9 * t = 60.\r<BR>\n" );
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document.write( "solve for t to get t = 60/9 = 6 and 2/3.\r<BR>\n" );
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document.write( "9 * (6 + 2/3) = 60 so that part checks out.<BR>\n" );
document.write( "your normal speed is 9 kmph and your normal time is 6 and 2/3 hours.\r<BR>\n" );
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document.write( "when you cut your speed by 3 kmph, then your speed is 6 kmph.<BR>\n" );
document.write( "your time is increased by 3 and 1/3 hours.\r<BR>\n" );
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document.write( "that makes you time equal to 6 and 2/3 + 3 and 1/3 = 10 hours.\r<BR>\n" );
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document.write( "rate * time becomes 6 * 10 = 60 km.\r<BR>\n" );
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document.write( "answer checks out and so is good.\r<BR>\n" );
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document.write( "i'm not quite sure what you were asked to solve here.\r<BR>\n" );
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document.write( "if it was just to factor the quadratic, then there are 3 basic methods you can choose.\r<BR>\n" );
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document.write( "one is use of the quadratic formula.\r<BR>\n" );
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document.write( "two is the box method.\r<BR>\n" );
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document.write( "three is factor by grouping.\r<BR>\n" );
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document.write( "four is the guess and check method.\r<BR>\n" );
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document.write( "i don't have time to show you how to do them, but here's some references.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/factquad.htm\" target = \"_blank\">http://www.purplemath.com/modules/factquad.htm</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/factquad3.htm\" target = \"_blank\">http://www.purplemath.com/modules/factquad3.htm</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/atv1/revfactorgrouping.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/atv1/revfactorgrouping.htm</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.regentsprep.org/regents/math/algtrig/atv1/revFactoring.htm\" target = \"_blank\">http://www.regentsprep.org/regents/math/algtrig/atv1/revFactoring.htm</a>\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut17_quad.htm\" target = \"_blank\">http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut17_quad.htm</a>\r<BR>\n" );
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document.write( "as you can see, there's lots of methods.\r<BR>\n" );
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document.write( "last one involves use of the quadratic formula.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.purplemath.com/modules/quadform.htm\" target = \"_blank\">http://www.purplemath.com/modules/quadform.htm</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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