document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=72846>Question 72846</A>: <I><SPAN STYLE=\"word-break: break-all;\"> During rush hour, Fernando can drive 35 miles using the side roads in the same time that it takes to travel 30 miles on the freeway. If Fernando's rate on the side roads is 9 mi/h faster than his rate on the freeway, find his rate on the side roads.\r<BR>\n" );
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document.write( "I came up with 65 and was wanting to check to see if this is right. Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #52135 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=52135\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Close to being right.<BR>\n" );
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document.write( "Let's use the equation D = R*T ... Distance = Rate * Time ... for both the freeway and side<BR>\n" );
document.write( "road trips.<BR>\n" );
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document.write( "We are told that the time is the same for both of these trips.  But if the speed on the<BR>\n" );
document.write( "freeway is called S, then the rate on the side roads is S+9.<BR>\n" );
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document.write( "The distance on the side road is 35 miles, and, as we stated above, the rate is S+9.<BR>\n" );
document.write( "So for the side road trip the distance equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35+=+%28S%2B9%29%2AT ALIGN=MIDDLE  ALT=\"35+=+%28S%2B9%29%2AT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Similarly, for the freeway trip the distance is 30 miles and the rate is S. So for this route<BR>\n" );
document.write( "the distance equation is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+S%2AT ALIGN=MIDDLE  ALT=\"30+=+S%2AT\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solve both of these equations for T. The side road equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+35%2F%28S%2B9%29 ALIGN=MIDDLE  ALT=\"T+=+35%2F%28S%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the freeway equation becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T+=+30%2FS ALIGN=MIDDLE  ALT=\"T+=+30%2FS\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Because the time is the same in both cases, the right sides of these equations must be <BR>\n" );
document.write( "equal. So we can write:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2F%28S%2B9%29+=+30%2FS ALIGN=MIDDLE  ALT=\"35%2F%28S%2B9%29+=+30%2FS\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "A short way of solving this is to multiply along both diagonals and set the two products<BR>\n" );
document.write( "equal.  In other words, multiply the numerator of one fraction by the denominator <BR>\n" );
document.write( "of the other and do the same for the other numerator and denominator pair.  In this case<BR>\n" );
document.write( "multiply the 35 time S and then multiply the 30 times (S+9). Then set the products <BR>\n" );
document.write( "equal to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2AS+=+30%2A%28S%2B9%29 ALIGN=MIDDLE  ALT=\"35%2AS+=+30%2A%28S%2B9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "do the distributive multiplying on the right side to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%2AS+=+30%2AS+%2B+270 ALIGN=MIDDLE  ALT=\"35%2AS+=+30%2AS+%2B+270\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "then subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2AS ALIGN=MIDDLE  ALT=\"30%2AS\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides and the equation is reduced to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2AS+=+270 ALIGN=MIDDLE  ALT=\"5%2AS+=+270\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide both sides by 5 and you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+54 ALIGN=MIDDLE  ALT=\"S+=+54\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  But this is the freeway speed and you<BR>\n" );
document.write( "were asked to find the speed on the side road which is 9 mph faster.  So add 9 to 54 and<BR>\n" );
document.write( "you get that the side road speed is 63 mph.<BR>\n" );
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document.write( "Hope this helps you to find the source of the difference in our answers.  You seem to<BR>\n" );
document.write( "have been pretty close so it's probably a minor mistake by one of us.<BR>\n" );
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