document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139174>Question 139174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me translate into a quadratic equation and solve.\r<BR>\n" );
document.write( "\n" );
document.write( "Steve traveled 200 miles at a certain speed. Had he gone 10 MPH faster, the trip would have taken 1 hour less. Find the speed of his vehicle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #101502 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=101502\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Steve traveled 200 miles at a certain speed. Had he gone 10 MPH faster, the trip would have taken 1 hour less. Find the speed of his vehicle.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let s = his actual speed<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(s+10) = his \"if\" speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Write a time equation: Time = dist/speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Actual time = Faster speed time + 1 hr<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fs ALIGN=MIDDLE  ALT=\"200%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28%28s%2B10%29%29 ALIGN=MIDDLE  ALT=\"200%2F%28%28s%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + 1<BR>\n" );
document.write( "Multiply equation by s(s+10) to get rid of the denominators:<BR>\n" );
document.write( "s(s+10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2Fs ALIGN=MIDDLE  ALT=\"200%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" > = s(s+10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200%2F%28%28s%2B10%29%29 ALIGN=MIDDLE  ALT=\"200%2F%28%28s%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + s(s+10)*1<BR>\n" );
document.write( "cancel the denominators out and you have:<BR>\n" );
document.write( "200(s+10) = 200s + s(s+10)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "200s + 2000 = 200s + s^2 + 10s<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Combine;<BR>\n" );
document.write( "0 = s^2 + 10s + 200s - 200s - 2000<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "s^2 + 10s - 2000 = 0<BR>\n" );
document.write( "Factors to:<BR>\n" );
document.write( "(s+50) (s-40) = 0<BR>\n" );
document.write( "The positive solution:<BR>\n" );
document.write( "s = +40 mph is his speed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check solution by finding the times<BR>\n" );
document.write( "200/40 = 5 hrs<BR>\n" );
document.write( "200/50 = 4 hrs </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );