document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117047>Question 117047</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bicyclist rode into the country for 5 hr.  In returning, her speed was 5 mi/h faster and the trip took 4 hr.  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 #85148 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=85148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use the equation:<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( "for the two parts of this problem.  D represents the distance traveled, R the rate or speed<BR>\n" );
document.write( "of the travel, and T the time spent traveling.<BR>\n" );
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document.write( "For the first part of the problem, call the unknown rate of travel S (standing for speed). And the <BR>\n" );
document.write( "problem tells you that the bicyclist rode out into the country for a time T equal to 5 hours.<BR>\n" );
document.write( "Putting these values into the Distance equation results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+S%2A5 ALIGN=MIDDLE  ALT=\"D+=+S%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "On the return trip the Rate is S + 5 because you are told that it is 5 miles per hour faster<BR>\n" );
document.write( "than on the ride out into the country. You are also told that the duration of the return<BR>\n" );
document.write( "ride is 4 hours. Putting these values into the Distance equation for the return ride results in:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+%28S+%2B+5%29%2A4 ALIGN=MIDDLE  ALT=\"D+=+%28S+%2B+5%29%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Do the distributed multiplication on the right side by multiplying the 4 times each of the<BR>\n" );
document.write( "two terms in the parentheses. This multiplication results in the Distance equation becoming:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+4S+%2B+20 ALIGN=MIDDLE  ALT=\"D+=+4S+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now recognize that the two distances ... the one going into the country and the one returning<BR>\n" );
document.write( "are equal. So the right sides of the two Distance equations must be equal. In equation form<BR>\n" );
document.write( "this is represented as:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5S+=+4S+%2B+20 ALIGN=MIDDLE  ALT=\"5S+=+4S+%2B+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Get rid of the 4S on the right side by subtracting 4S from both sides. Subtracting 4S<BR>\n" );
document.write( "from both sides reduces the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+20 ALIGN=MIDDLE  ALT=\"S+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This tells us that the bicyclist rode at a speed of 20 miles per hour going out into the country,<BR>\n" );
document.write( "and, since the rate or speed was 5 miles per hour faster on the return trip, the speed on <BR>\n" );
document.write( "the return trip was 25 miles per hour.<BR>\n" );
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document.write( "And as add information (not required by the problem) the distance she rode into the country<BR>\n" );
document.write( "can be determined by multiplying her speed of 20 miles per hour on the outbound trip by the 5 hours<BR>\n" );
document.write( "she spent on this portion of the trip. 20 times 5 is 100 miles. On the return trip she rode<BR>\n" );
document.write( "at a speed of 25 miles per hour for hours, and 25 times 4 also equals 100 miles, just as it is<BR>\n" );
document.write( "supposed to since the distances are equal in both directions.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better and helps you to understand the<BR>\n" );
document.write( "equation that says Distance equals Rate times Time.<BR>\n" );
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