document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=963427>Question 963427</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suzanne rides the chairlift to the top of a 4 mile hill, then skis down at 8 miles per hour faster than lift travels. The trip is 8 minutes faster than the ride up. Find her average speed for the entire trip. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588585 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=588585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "R is equal to the rate of speed on the way up.<BR>\n" );
document.write( "R + 8 is equal to the rate of speed on the way down.\r<BR>\n" );
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document.write( "T is equal to the time it takes to get to the top from the bottom.<BR>\n" );
document.write( "T - 8/60 is equal to the the time it takes to get to the bottom from the top.\r<BR>\n" );
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document.write( "you needed to convert everything to either minutes or hours.<BR>\n" );
document.write( "i chose hours.<BR>\n" );
document.write( "8/60 hours is equal to 8 minutes.\r<BR>\n" );
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document.write( "since rate * time is equal to distance, then:\r<BR>\n" );
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document.write( "R*T = 4 on the way up.<BR>\n" );
document.write( "(R+8) * (T - 8/60) = 4 on the way down.\r<BR>\n" );
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document.write( "you solve each of these equations for R to get:\r<BR>\n" );
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document.write( "R = 4/T from the equation for going up.<BR>\n" );
document.write( "R = 4/(T-8/60) - 8 from the equation for coming down.\r<BR>\n" );
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document.write( "since both expressions on the right side of the equation are equal to R, you can set them equal to each other to get:\r<BR>\n" );
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document.write( "4/T = (4/(T-8/60)) - 8\r<BR>\n" );
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document.write( "you then solve for T to get T = 1/3 of an hour.\r<BR>\n" );
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document.write( "the solving results in a quadratic equation of 480T^2 - 64T - 32 = 0 which can then be factored to get 15T^2 - 2T - 1 = 0 which can then be factored to get (5T+1) * (3T-1) = 0 which can then be solved for T to get T = -1/5 or T = 1/3.<BR>\n" );
document.write( "Since T can't be minus, the only possible solution is T = 1/3.\r<BR>\n" );
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document.write( "once you've done that, you then solve for R to get R = 12.\r<BR>\n" );
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document.write( "For the ride up, R * T = 4 becomes 1/3 * 12 = 4 miles.\r<BR>\n" );
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document.write( "For the ride down, (R+8) * (T - 8/60) becomes (12+8) * (1/3 - 8/60) which becomes 20 * (20/60 - 8/60) which becomes 20 * 12/60 which becomes 20 * 1/5 which becomes 20/5 which becomes 4.\r<BR>\n" );
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document.write( "T = 1/3 of an hour and R = 12 miles per hour is confirmed to be good.\r<BR>\n" );
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document.write( "the total time it took to go up and down is 1/3 of an hour to go up + 12/60 of an hour to go down which makes the total time equal to 1/3 + 12/60 = 20/60 + 12/60 = 32/60 = 8/15 of an hour.\r<BR>\n" );
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document.write( "the average speed for the total trip up and down is therefore 8 / (8/15) which is equal to 8 * 15/8 which is equal to 15 miles per hour.\r<BR>\n" );
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document.write( "this is derived from the rate * time = distance formula again.\r<BR>\n" );
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document.write( "distance round trip is 8.<BR>\n" );
document.write( "time round trip is 8/15 of an hour.<BR>\n" );
document.write( "R * T = 8 becomes R * 8/15 = 8 which becomes R = 8 * 15/8 which becomes R = 15.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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