document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7621>Question 7621</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help, I have been trying to figure this out for 3 days.  I know I should use x for Elizabeth's speed and x+5 for Rick's speed but I am having trouble coming up with the equation to solve.  \r<BR>\n" );
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document.write( "Elizabeth and her husband Rick bicycled cross-country together. One morning, Elizabeth rode 40 miles.  By traveling only 5 miles per hour faster and putting in one more hour, Rick covered twice the distance Elizabeth covered.  What is the speed of each cyclist?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4203 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=4203\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As you say, <BR>\n" );
document.write( "let Elizabeth speed = x (in miles)<BR>\n" );
document.write( "let Rick's speed = x+5\r<BR>\n" );
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document.write( "Elizabeth rode 40 miles, Rick rode 80 miles\r<BR>\n" );
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document.write( "Elizabeth's time = t (in hours)<BR>\n" );
document.write( "Rick's time = t+1\r<BR>\n" );
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document.write( "we want to find their speeds, but we also do not know their times, so we will get an equation for each based upon speed = distance/time and then re-arrange for t and then equate, to get rid of t. This will just leave one equation with the unknown, x, which we will solve. \r<BR>\n" );
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document.write( "That is the theory :-)\r<BR>\n" );
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document.write( "Right then, first Elizabeth:\r<BR>\n" );
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document.write( "speed = distance/time <BR>\n" );
document.write( "x = 40/t --> t = 40/x\r<BR>\n" );
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document.write( "Now Rick:\r<BR>\n" );
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document.write( "speed = distance/time<BR>\n" );
document.write( "x+5 = 80/(t+1)<BR>\n" );
document.write( "t+1 = 80/(x+5)<BR>\n" );
document.write( "t = 80/(x+5) - 1\r<BR>\n" );
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document.write( "so we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fx+=+80%2F%28x%2B5%29+-+1 ALIGN=MIDDLE  ALT=\"40%2Fx+=+80%2F%28x%2B5%29+-+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now it is just algebraic manipulation...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fx+%2B+1+=+80%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"40%2Fx+%2B+1+=+80%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fx+%2B+x%2Fx+=+80%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"40%2Fx+%2B+x%2Fx+=+80%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B40%29%2Fx+=+80%2F%28x%2B5%29 ALIGN=MIDDLE  ALT=\"%28x%2B40%29%2Fx+=+80%2F%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Now cross multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B40%29%28x%2B5%29+=+80x ALIGN=MIDDLE  ALT=\"%28x%2B40%29%28x%2B5%29+=+80x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+45x+%2B+200+=+80x ALIGN=MIDDLE  ALT=\"x%5E2+%2B+45x+%2B+200+=+80x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+35x+%2B+200+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+35x+%2B+200+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "put this into the quadratic formula to give <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2835+%2B-+5sqrt%2817%29%29%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2835+%2B-+5sqrt%2817%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This means that x = 27.8 mph or x=7.192mph.\r<BR>\n" );
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document.write( "For a person on a cycle, i would suggest that 7.192mph is the answer required. Then Rick's speed would be 12.192mph.\r<BR>\n" );
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document.write( "Please check my working though, just in case i have made an error somewhere.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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