document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=761850>Question 761850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After making a trip of 126 miles, a lady found that if she had increased her average speed by 8mph, she could have made the trip in 1 hour less time. Find her original speed.\r<BR>\n" );
document.write( "\n" );
document.write( "My 2 equations:<BR>\n" );
document.write( "original: 126=(s+8)*(t-1)<BR>\n" );
document.write( "theoretical trip: 126=s*t<BR>\n" );
document.write( "After I plug the 2nd equation into the first I do not know what to do. <BR>\n" );
document.write( "126=(s+8)*((126/s)-1)<BR>\n" );
document.write( "Please help! Thank You Thank You Thank You!!!!! -Abby </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463539 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=463539\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> After making a trip of 126 miles, a lady found that if she had<BR>\n" );
document.write( " increased her average speed by 8mph, she could have made the trip<BR>\n" );
document.write( " in 1 hour less time.<BR>\n" );
document.write( " Find her original speed.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let's try it this way.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = original speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+8) = her increase speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation: time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Original time - faster speed time = 1 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126%2Fs ALIGN=MIDDLE  ALT=\"126%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=126%2F%28%28s%2B8%29%29 ALIGN=MIDDLE  ALT=\"126%2F%28%28s%2B8%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1<BR>\n" );
document.write( "multiply by s(s+8) cancel the denominators, resulting in<BR>\n" );
document.write( "126(s+8) - 126s = s(s+8)<BR>\n" );
document.write( "126s + 1008 - 126s = s^2 + 8s<BR>\n" );
document.write( "combine all this, we have a quadratic equation of:<BR>\n" );
document.write( "s^2 + 8s - 1008 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(s+36)(s-28) = 0<BR>\n" );
document.write( "the positive solution is all we need here<BR>\n" );
document.write( "s = 28 mph is the original speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can check this by finding the time at each speed<BR>\n" );
document.write( "126/28 = 4.5 hrs<BR>\n" );
document.write( "126/36 = 3.5 hrs (8mph faster)<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "time dif: 1 hr  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );