document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=937584>Question 937584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new automatic machine can do a job in 1 hour less than an older machine. Together they can do the same job in 1.2 hours. How long would it take each machine to do the job alone?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #571024 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=571024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x = time for old machine<BR>\n" );
document.write( "y = time for new machine<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = x - 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "r = w/t<BR>\n" );
document.write( "rates are additive:<BR>\n" );
document.write( "r = 1/x + 1/y<BR>\n" );
document.write( "t = w/r<BR>\n" );
document.write( "t = 1/(1/x + 1/y)<BR>\n" );
document.write( "1.2 = 1/(1/x + 1/y)<BR>\n" );
document.write( "1.2(1/x + 1/y) = 1<BR>\n" );
document.write( "1.2/x + 1.2/y = 1<BR>\n" );
document.write( "1.2y/xy + 1.2x/xy = 1<BR>\n" );
document.write( "1.2y + 1.2x = xy<BR>\n" );
document.write( "1.2(y + x) = xy<BR>\n" );
document.write( "---<BR>\n" );
document.write( "substitute y = x - 1<BR>\n" );
document.write( "---<BR>\n" );
document.write( "1.2(x - 1 + x) = x(x - 1)<BR>\n" );
document.write( "1.2(2x - 1) = xx - x<BR>\n" );
document.write( "2.4x - 1.2 = xx - x<BR>\n" );
document.write( "xx - x - 2.4x + 1.2 = 0<BR>\n" );
document.write( "xx - 3.4x + 1.2 = 0<BR>\n" );
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document.write( "the above quadratic equation is in standard form, with a=1, b=-3.4 and c=1.2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to solve the quadratic equation, by using the quadratic formula, copy and paste this:<BR>\n" );
document.write( "1 -3.4 1.2<BR>\n" );
document.write( "into this solver: https://sooeet.com/math/quadratic-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the quadratic has two real roots at:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "x = 0.4<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the root x=0.4 makes y negative and doesn't fit the problem statement, so use the root x=3:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "x = 3<BR>\n" );
document.write( "y = x - 1<BR>\n" );
document.write( "y = 2<BR>\n" );
document.write( "---<BR>\n" );
document.write( "answer:<BR>\n" );
document.write( "x = time for old machine = 3 hours<BR>\n" );
document.write( "x = time for new machine = 2 hours<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Free algebra tutoring live chat:<BR>\n" );
document.write( "https://sooeet.com/chat.php?gn=algebra<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 with quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve systems of linear equations up to 6-equations 6-variables:<BR>\n" );
document.write( "https://sooeet.com/math/system-of-linear-equations-solver.php<BR>\n" );
document.write( "--- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );