document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=70733>Question 70733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bicyclist rode into the country for 5 h. In returning, her<BR>\n" );
document.write( "speed was 5 mi/h faster and the trip took 4 h. What was her speed each way? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #50498 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=50498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We'll use the basic equation that says the distance (D) that you travel is equal to the rate<BR>\n" );
document.write( "or speed that you are going (R) times the Time (T) that you use.  In equation form this is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+R%2AT ALIGN=MIDDLE  ALT=\"D+=+R%2AT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the trip out this bicyclist rode at some unknown rate (R) and she rode for 5 hours.<BR>\n" );
document.write( "Substituting these values into the equation results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+R%2A5 ALIGN=MIDDLE  ALT=\"D+=+R%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the way back she boosted her rate by 5 mph.  Therefore, her new rate was R+5.  She rode<BR>\n" );
document.write( "for 4 hours.  The equation that results is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+%28R%2B5%29%2A4 ALIGN=MIDDLE  ALT=\"D+=+%28R%2B5%29%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ". <BR>\n" );
document.write( "But the distance she traveled out is the same distance that she traveled on the way back.<BR>\n" );
document.write( "This means that the left side of our two equations are equal.  Because of this we can<BR>\n" );
document.write( "site the right side equal also. To be a little more conventional let's write R*5 as 5*R and<BR>\n" );
document.write( "(R+5)*4 as 4*(R+5). In equation form the equality of the right sides is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2AR+=+4%2A%28R%2B5%29 ALIGN=MIDDLE  ALT=\"5%2AR+=+4%2A%28R%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Multiplying out the right side results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2AR+=+4%2AR+%2B+20 ALIGN=MIDDLE  ALT=\"5%2AR+=+4%2AR+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Subtract 4*R from both sides and the equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R+=+20 ALIGN=MIDDLE  ALT=\"R+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This means that she rode out at 20 mph and as a result her return rate, 5 mph faster, was<BR>\n" );
document.write( "25 mph.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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