document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=315203>Question 315203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Justin recently drove to see his parents who live 390 miles away. on his way there his average speed was 11 mph faster than on his way home (he ran into some bad weather) if justin spent a total of 13 hours driving find the two rates </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225513 by </B><A HREF=/tutors/aboutme.mpl?userid=CharlesG2><B>CharlesG2(834)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CharlesG2><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=225513\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Justin recently drove to see his parents who live 390 miles away. on his way there his average speed was 11 mph faster than on his way home (he ran into some bad weather) if justin spent a total of 13 hours driving find the two rates\r<BR>\n" );
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document.write( "Distance D = Rate R * Time T<BR>\n" );
document.write( "d1 = distance to get there, r1 = rate to get there, t1 = time to get there<BR>\n" );
document.write( "d2 = distance to get back, r2 = rate to get back, t2 = time to get back<BR>\n" );
document.write( "d1 = d2 = 390 miles, r1 = r2 + 11 mph, t1 = 13 hours - t2<BR>\n" );
document.write( "way there to get r2:<BR>\n" );
document.write( "390 = (r2 + 11) * (13 - t2)<BR>\n" );
document.write( "390/(13 - t2) = r2 + 11<BR>\n" );
document.write( "390/(13 - t2) - 11 = r2<BR>\n" );
document.write( "(390 - 11(13 - t2))/(13 - t2) = r2<BR>\n" );
document.write( "(390 - 143 + 11t2)/(13 - t2) = r2<BR>\n" );
document.write( "(11t2 + 247)/(13 - t2) = r2<BR>\n" );
document.write( "way back to get t2:<BR>\n" );
document.write( "390 = (11t2 + 247)/(13 - t2) * t2<BR>\n" );
document.write( "390 = (11(t2)^2 + 247t2)/(13 - t2)<BR>\n" );
document.write( "390(13 - t2) = 11(t2)^2 + 247t2<BR>\n" );
document.write( "5070 - 390t2 = 11(t2)^2 + 247t2<BR>\n" );
document.write( "-11(t2)^2 - 390t2 - 247t2 + 5070 = 0 (rearranged terms)<BR>\n" );
document.write( "-11(t2)^2 - 637t2 + 5070 = 0<BR>\n" );
document.write( "11(t2)^2 + 637t2 - 5070 = 0 (divided both sides by -1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t2+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"t2+=+%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( "a = 11, b = 637, c = -5070<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t2+=+%28-637+%2B-+sqrt%28+405769+%2B+223080+%29%29%2F22+ ALIGN=MIDDLE  ALT=\"t2+=+%28-637+%2B-+sqrt%28+405769+%2B+223080+%29%29%2F22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t2+=+%28-637+%2B-+sqrt%28628849%29%29%2F22+ ALIGN=MIDDLE  ALT=\"t2+=+%28-637+%2B-+sqrt%28628849%29%29%2F22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t2+=+%28-637+%2B-+793%29%2F22+ ALIGN=MIDDLE  ALT=\"t2+=+%28-637+%2B-+793%29%2F22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(the result that involves -637 - 793 is thrown out that would result in a negative answer)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t2+=+%28-637+%2B+793%29%2F22+ ALIGN=MIDDLE  ALT=\"t2+=+%28-637+%2B+793%29%2F22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t2+=+156%2F22+ ALIGN=MIDDLE  ALT=\"t2+=+156%2F22+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "t2 = 156/22 = 78/11 = 7 1/11 = 7.091 to 3 places hours<BR>\n" );
document.write( "t1 = 13 - t2 = 143/11 - 78/11 = 65/11 = 5 10/11 = 5.909 to 3 places hours<BR>\n" );
document.write( "390 = r1 * 65/11<BR>\n" );
document.write( "(390 * 11)/65 = r1<BR>\n" );
document.write( "4290/65 = 858/13 = 66 mph = r1<BR>\n" );
document.write( "390 = r2 * 78/11<BR>\n" );
document.write( "(390 * 11)/78 = r2<BR>\n" );
document.write( "4290/78 = 2145/39 = 55 mph = r2<BR>\n" );
document.write( "does r1 = r2 + 11? --> 55 + 11 = 66 --> yes\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );