document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818151>Question 818151</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cyclist traveled 60 mi at a constant rate before reducing the speed by 7 mph. Another 40 mi was traveled at the reduced speed. The total time for the 100-mile trip was 9 h. Find the rate during the first 60 mi. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492388 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=492388\">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( "total trip:<BR>\n" );
document.write( "ta + tb = 9<BR>\n" );
document.write( "tb = 9 - ta<BR>\n" );
document.write( "s = 100 / 9 = 11.11 mph<BR>\n" );
document.write( "---<BR>\n" );
document.write( "segment a:<BR>\n" );
document.write( "sa = 60 / ta<BR>\n" );
document.write( "---<BR>\n" );
document.write( "segment b:<BR>\n" );
document.write( "sb = 40 / tb<BR>\n" );
document.write( "sb = sa - 7<BR>\n" );
document.write( "40 / tb = sa - 7<BR>\n" );
document.write( "40 = tb(sa - 7)<BR>\n" );
document.write( "40 = (9 - ta)(sa - 7)<BR>\n" );
document.write( "40 = 9sa - 63 - sa*ta + 7ta<BR>\n" );
document.write( "---<BR>\n" );
document.write( "sa = 60 / ta<BR>\n" );
document.write( "sa*ta = 60<BR>\n" );
document.write( "---<BR>\n" );
document.write( "40 = 9sa - 63 - sa*ta + 7ta<BR>\n" );
document.write( "40 = 9(60/ta) - 63 - 60 + 7ta<BR>\n" );
document.write( "40 = 540/ta - 123 + 7ta<BR>\n" );
document.write( "163 = 540/ta + 7ta<BR>\n" );
document.write( "163 = 540/ta + 7ta^2/ta<BR>\n" );
document.write( "163ta = 540 + 7ta^2<BR>\n" );
document.write( "7ta^2 - 163ta + 540 = 0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the above quadratic equation is in standard form, with a=7, b=-163, and c=540<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to solve the quadratic equation, by using the quadratic formula, plug this:<BR>\n" );
document.write( "7 -163 540<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( "ta = 19.2857143<BR>\n" );
document.write( "ta = 4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the large root (19.3 hours) exceeds the total time for the trip (9 hours), so use the small root (4 hours):<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "ta = 4 hours<BR>\n" );
document.write( "tb = 5 hours<BR>\n" );
document.write( "sa = 60 / 4 = 15 mph<BR>\n" );
document.write( "sb = 40 / 5 = 8 mph<BR>\n" );
document.write( "---<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "sa - sb = 7 mph (correct!)<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" );