document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1159329>Question 1159329</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bert traveled 72 miles across the state through rain at a reasonable speed.  If it had been sunny, he would have driven an average of 20 miles per hour faster, and would have arrived at his destination 24 minutes sooner.  How long did his trip take him in the rain? How fast was he driving in the rain?<BR>\n" );
document.write( "Hint: First solve a quadratic equation. Then write two equations with two unknowns. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #782323 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=782323\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Bert traveled 72 miles across the state through rain at a reasonable speed.<BR>\n" );
document.write( " If it had been sunny, he would have driven an average of 20 miles per hour faster, and would have arrived at his destination 24 minutes sooner.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let s = speed in the rain<BR>\n" );
document.write( "let t = drive time in the rain<BR>\n" );
document.write( "change 24 min 24/60 = .4 hrs, then<BR>\n" );
document.write( "(s+20) = sunny speed<BR>\n" );
document.write( "(t-.4) = sunny driving time)<BR>\n" );
document.write( "Two distance equations<BR>\n" );
document.write( "s*t = 72<BR>\n" );
document.write( "for substitution<BR>\n" );
document.write( "s = 72/t<BR>\n" );
document.write( "and<BR>\n" );
document.write( "(t-.4)*(s+20) = 72<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "ts + 20t - .4s - 8 = 72<BR>\n" );
document.write( "we know ts = 72<BR>\n" );
document.write( "72 + 20t - .4s - 8 = 72<BR>\n" );
document.write( "-72 from both sided <BR>\n" );
document.write( "20t - .4s - 8 = 0<BR>\n" );
document.write( "simplify, divide by .4<BR>\n" );
document.write( "50t - s - 20<BR>\n" );
document.write( "replace s with (72/t)<BR>\n" );
document.write( "50t - 72/t - 20 = 0<BR>\n" );
document.write( "multiply by t<BR>\n" );
document.write( "50t^2 - 72 - 20t = 0<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "50t^2 - 20t - 72 = 0<BR>\n" );
document.write( "Using the quadratic formula I got a postive solution of<BR>\n" );
document.write( "t = 1.41655 hrs or 1 + .41655*60 = 1 hr 25 min, his time in the rain<BR>\n" );
document.write( ":<BR>\n" );
document.write( "  How fast was he driving in the rain?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72%2F1.41655 ALIGN=MIDDLE  ALT=\"72%2F1.41655\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 50.8 mph <BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this, find his sunny speed. 50.8 + 20 = 70.8 mph<BR>\n" );
document.write( "Find his sunny time: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72%2F70.8 ALIGN=MIDDLE  ALT=\"72%2F70.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.0169 or 1 + .0169*60 = 1 hr 1 min<BR>\n" );
document.write( "Which ia 24 min faster than the time in rain\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hint: First solve a quadratic equation. Then write two equations with two unknowns. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );