document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187209>Question 187209</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0321233832/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This is from a text book and I cannot figure how to set it up and answer it.<BR>\n" );
document.write( "CAR TRIP.  During the first part of a trip, Trudy's Honda traveled 120 mi at a certain speed.  Trudy then drove another 100 miles at a speed that was 10 mph slower.  If the total time of Trudy's trip was 4 hr, what was her speed on each part of the trip?  I am stumped at the moment.  Thank you for your help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140370 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=140370\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "WOULD IT HELP IF I SET IT UP AND YOU ANSWER IT?  OK.  I'LL SET IT UP.\r<BR>\n" );
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document.write( "Distanced(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r\r<BR>\n" );
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document.write( "Let r=her speed during the first part of the trip<BR>\n" );
document.write( "Then r-10= her speed during the second part of the trip<BR>\n" );
document.write( "time for first part of trip=120/r<BR>\n" );
document.write( "time for second part of trip=100/(r-10)<BR>\n" );
document.write( "And we are told that the sum of the above two times equals 4 hrs, so:\r<BR>\n" );
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document.write( "120/r +100/(r-10)=4  multiply each term by r(r-10)<BR>\n" );
document.write( "120(r-10)+100r=4r(r-10)  get rid of parens<BR>\n" );
document.write( "120r-1200+100r=4r^2-40r  subtract 4r^2 from and add 40r to both sides<BR>\n" );
document.write( "120r-1200+100r-4r^2+40r=0  collect like terms<BR>\n" );
document.write( "-4r^2+260r-1200=0  divide each term by -4<BR>\n" );
document.write( "r^2-65r+300=0  quadratic in standard form and it can be factored:<BR>\n" );
document.write( "(r-60)(r-5)=0<BR>\n" );
document.write( "By inspection, we can see that 5 is no good because when we subtract 10 from it, we get a negative speed and that's not good.\r<BR>\n" );
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document.write( "I think you can take it from here\r<BR>\n" );
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document.write( "Hope this helps---ptaylor\r<BR>\n" );
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document.write( " </SPAN>\n" );
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