document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=976017>Question 976017</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Sarah travels for 100 miles and then decreases her rate of travel by 5 mph and continued the remaining 300 miles of her trip. If the total trip took 7 hours and 40 minutes, at what two speeds did she travel? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #597780 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=597780\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sarah travels for 100 miles and then decreases her rate of travel by 5 mph and continued the remaining 300 miles of her trip.<BR>\n" );
document.write( " If the total trip took 7 hours and 40 minutes, at what two speeds did she travel?<BR>\n" );
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document.write( "Let s = the original speed for the 1st 100 mi<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s-5) = the speed for the remaining 300 mi<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Change 7 hrs 40 min to hrs: 7 + 40/60 = 7<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23%2F3 ALIGN=MIDDLE  ALT=\"23%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation; time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100%2Fs ALIGN=MIDDLE  ALT=\"100%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2F%28%28s-5%29%29 ALIGN=MIDDLE  ALT=\"300%2F%28%28s-5%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23%2F3 ALIGN=MIDDLE  ALT=\"23%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply by 3s(s-5), cancel the denominators and you have<BR>\n" );
document.write( "3(s-5)*100 + 3s(300) = 23s(s-5)<BR>\n" );
document.write( "300(s-5) + 3s(300) = 23s^2 - 115s<BR>\n" );
document.write( "300s - 1500 + 900s = 23s^2 - 115s<BR>\n" );
document.write( "Combine like terms on the right<BR>\n" );
document.write( "0 = 23s^2 - 115s - 1200s + 1500<BR>\n" );
document.write( "23s^2 - 1315s + 1500 = 0<BR>\n" );
document.write( "use the quadratic formula to find s: a=23; b=-1315; c=1500<BR>\n" );
document.write( "I got the reasonable solution of <BR>\n" );
document.write( "s = 56 mph the 1st 100 mi<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "51 mph the last 300 mi (5 mph slower)<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Confirm this by finding the actual time at each speed<BR>\n" );
document.write( "100/56 = 1.79 hrs<BR>\n" );
document.write( "300/51 = 5.88 hrs <BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "total time: 7.67 hrs which is about 7 hrs 40 min </SPAN>\n" );
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