document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=816658>Question 816658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the speed of a train if an increase of 6 kph lowers the time for a journey of 72 km by 10 minutes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #491648 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=491648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> s = d / t<BR>\n" );
document.write( "d = s * t<BR>\n" );
document.write( "---<BR>\n" );
document.write( "D = 72 = st<BR>\n" );
document.write( "D = (s + 6)(t - 1/6)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "st = (s + 6)(t - 1/6)<BR>\n" );
document.write( "st = st - (1/6)s + 6t - 1<BR>\n" );
document.write( "0 = -(1/6)s + 6t - 1<BR>\n" );
document.write( "0t = -(1/6)st + 6tt - t<BR>\n" );
document.write( "0 = -(1/6)72 + 6t^2 - t<BR>\n" );
document.write( "0 = 6t^2 - t - 12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the above quadratic equation is in standard form, with a=6, b=-1, and c=-12<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to solve the quadratic equation, plug this:<BR>\n" );
document.write( "6 -1 -12<BR>\n" );
document.write( "into this: https://sooeet.com/math/quadratic-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the roots of the quadratic are:<BR>\n" );
document.write( "t = 1.5<BR>\n" );
document.write( "t = -1.33333333<BR>\n" );
document.write( "---<BR>\n" );
document.write( "negative time doesn't make sense for this problem, so use the positive root:<BR>\n" );
document.write( "t = 1.5 hours<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Answer: <BR>\n" );
document.write( "the speed of a train: 72 km / 1.5 hours = 48 kph<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Convert fractions, decimals, and percents:<BR>\n" );
document.write( "https://sooeet.com/math/fraction-decimal-percent.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Calculate and graph the linear regression of any data set:<BR>\n" );
document.write( "https://sooeet.com/math/linear-regression.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );