document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=718562>Question 718562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Thank you in advance if you are able to help solve the word problem for me. The question is, \"Your commute to De Anza from San Francisco is 40 miles and your average rate of your return trip is 30 miles per hour faster than your average rate of going to De Anza. If the round trip takes 2 hours, what is your average rate coming to school? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #441006 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=441006\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your commute to De Anza from San Francisco is 40 miles, and your average rate of your return trip is 30 miles per hour faster, than your average rate of going to De Anza.<BR>\n" );
document.write( " If the round trip takes 2 hours, what is your average rate coming to school?<BR>\n" );
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document.write( "let s = your speed to Anza<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+30) = return trip speed<BR>\n" );
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document.write( "Write a time equation; time = dist/speed<BR>\n" );
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document.write( "To time + return time = 2 hrs<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2Fs ALIGN=MIDDLE  ALT=\"40%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40%2F%28%28s%2B30%29%29 ALIGN=MIDDLE  ALT=\"40%2F%28%28s%2B30%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2 <BR>\n" );
document.write( "multiply equation by s(s+30), resulting in:<BR>\n" );
document.write( "40(s+30) + 40s = 2s(s+30)<BR>\n" );
document.write( "40s + 1200 + 40s = 2s^2 + 60s<BR>\n" );
document.write( "arrange as a quadratic equation on the right<BR>\n" );
document.write( "0 = 2s^2 + 60s - 80s - 1200<BR>\n" );
document.write( "2s^2 - 20s - 1200 = 0<BR>\n" );
document.write( "Simplify, divide by 2<BR>\n" );
document.write( "s^2 - 10s - 600 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(s+20)(s-30) = 0<BR>\n" );
document.write( "the positive solution is all we want here<BR>\n" );
document.write( "s = 30 mph to Anza<BR>\n" );
document.write( "and<BR>\n" );
document.write( "30 + 30 = 60 mph return<BR>\n" );
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document.write( "See if that checks out, find the actual time each way<BR>\n" );
document.write( "40/30 = 1.33 hrs<BR>\n" );
document.write( "40/60 = .67 hrs<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "total time: 2 hrs </SPAN>\n" );
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