document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43929>Question 43929</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0201719665/algebrahomeworkh>elementry and intermediate algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> please help with this problem:<BR>\n" );
document.write( " On a bicycle trip,Maria averaged 5 miles per hour faster for the first 60 miles than she did for the last 75 miles. The entire trip took 8 hours. Find her rate for the first 60 miles. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28862 by </B><A HREF=/tutors/aboutme.mpl?userid=adamchapman><B>adamchapman(301)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=adamchapman><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=28862\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write what we already know in equation form.<BR>\n" );
document.write( "Let's use these symbols for our unknown variables:<BR>\n" );
document.write( "x=rate for first 60 miles<BR>\n" );
document.write( "y=rate for last 75 miles\r<BR>\n" );
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document.write( "We know from the question that x=y+5,<BR>\n" );
document.write( "rearranging gives y=x-5\r<BR>\n" );
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document.write( "time = distance/speed<BR>\n" );
document.write( "We know that the total time spent was 8 hours, so we can write:<BR>\n" );
document.write( "8 = (60/x) + (75/y)<BR>\n" );
document.write( "If we substitute y=x-5, we get:<BR>\n" );
document.write( "8 = (60/x) + (75/(x-5))<BR>\n" );
document.write( "multiplying both sides by (x-5):<BR>\n" );
document.write( "8(x-5)=(60(x-5)/x)+75<BR>\n" );
document.write( "multiplying both sides by (x):<BR>\n" );
document.write( "8x(x-5)=60(x-5)+75x<BR>\n" );
document.write( "rearranging:<BR>\n" );
document.write( "8x^2-40x=60x-300+75x<BR>\n" );
document.write( "8x^2-175x+300=0<BR>\n" );
document.write( "using the quadratic solver: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ;<BR>\n" );
document.write( "x=1.875 or x=20<BR>\n" );
document.write( "y is 5 less than x (y=x-5), and if x was 1.85, Maria would be cycling backwards for the second part of her journey! <BR>\n" );
document.write( "Logic tells us that x must be 20 mph, implying that y=15mph\r<BR>\n" );
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document.write( "I hope this helps. If you have any other problems, please dont hesitate to contact me at adam.chapman@student.manchester.ac.uk \r<BR>\n" );
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document.write( " </SPAN>\n" );
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