document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=481446>Question 481446</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A car traveled 510 miles in 8 hours. The car traveled the first 300 miles at a constant rate before increasing its speed by 10 mph. Then it traveled another 210 miles at the increased speed. Find the rate of the car for the first 300 miles </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329718 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=329718\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A car traveled 510 miles in 8 hours.<BR>\n" );
document.write( "The car traveled the first 300 miles at a constant rate before increasing its speed by 10 mph.<BR>\n" );
document.write( " Then it traveled another 210 miles at the increased speed.<BR>\n" );
document.write( " Find the rate of the car for the first 300 miles.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let s = the speed for the 1st 300 mi<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+10) = speed for the remaining 210 mi<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation: time = dist/speed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2Fs ALIGN=MIDDLE  ALT=\"300%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2F%28%28s%2B10%29%29 ALIGN=MIDDLE  ALT=\"210%2F%28%28s%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8<BR>\n" );
document.write( ":<BR>\n" );
document.write( "multiply by s(s+10) and cancel the denominators, resulting in:<BR>\n" );
document.write( "300(s+10) + 210s = 8s(s+10)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "300s + 3000 + 210s = 8s^2 + 80s<BR>\n" );
document.write( "510s + 3000 = 8s^2 + 80s<BR>\n" );
document.write( "Combine like terms on the right<BR>\n" );
document.write( "0 = 8s^2 + 80s - 510s - 3000<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "8s^2 - 430s - 3000 = 0<BR>\n" );
document.write( "Find s using the quadratic formula; a=8, b=-430, c=-3000<BR>\n" );
document.write( "the positive solution: 60 mph<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check by finding the total of the times<BR>\n" );
document.write( "300/60 = 5 hrs<BR>\n" );
document.write( "210/70 = 3 hrs<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "total: 8 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );