document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206942>Question 206942</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two technicians can complete a mailing in 3 hours when working together. alone, one can complete the mailing 2 hours faster than the other. how long will it take each person to complete the mailing alone? compute answer to two decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #156453 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=156453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let x = rate of first technician<BR>\n" );
document.write( "let y = rate of second technician.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "working together they can complete a mailing in 3 hours.<BR>\n" );
document.write( "(x + y) * 3 = 1<BR>\n" );
document.write( "(x + y) is their combined rate.<BR>\n" );
document.write( "3 = number of hours<BR>\n" );
document.write( "1 = units produced.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "they produced 1 unit of mailing in 3 hours working together.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let the first technician be the faster mailer.<BR>\n" );
document.write( "the first technician works at a rate of x mailings per hour.<BR>\n" );
document.write( "the second technician works at a rate of y mailings per hour. <BR>\n" );
document.write( "-----<BR>\n" );
document.write( "alone, the first technician can complete the mailing 2 hours faster than the other.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "let h = amount of time in hours it takes for the first technician to complete the mailing.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "x * h = 1 mailing<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since the first technician can complete the mailing in 2 hours less than the second technician, then (h+2) represents the time it takes the second technician to complete the mailing.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "y * (h+2) = 1 mailing<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since x * h = 1, then x = (1/h) which looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fh%29 ALIGN=MIDDLE  ALT=\"%281%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since y * (h+2) = 1, then y = (1/(h+2)) which looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%28h%2B2%29%29 ALIGN=MIDDLE  ALT=\"%281%2F%28h%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "formula of (x+y)*3 = 1 becomes ((1/h) + (1/(h+2))) * 3 = 1<BR>\n" );
document.write( "this looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Fh%29+%2B+%281%2F%28h%2B2%29%29%29+%2A+3+=+1 ALIGN=MIDDLE  ALT=\"%28%281%2Fh%29+%2B+%281%2F%28h%2B2%29%29%29+%2A+3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "multiply both sides of this equation by (h)*(h+2) to get ((h+2) + (h)) * 3 = (h)*(h+2)<BR>\n" );
document.write( "this looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28h%2B2%29+%2B+%28h%29%29+%2A+3+=+%28h%29%2A%28h%2B2%29 ALIGN=MIDDLE  ALT=\"%28%28h%2B2%29+%2B+%28h%29%29+%2A+3+=+%28h%29%2A%28h%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this becomes 6h + 6 = h^2 + 2h which looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6h+%2B+6+=+h%5E2+%2B+2h ALIGN=MIDDLE  ALT=\"6h+%2B+6+=+h%5E2+%2B+2h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this eventually results in h^2 - 4h - 6 = 0 which looks like <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+-+4h+-+6+=+0 ALIGN=MIDDLE  ALT=\"h%5E2+-+4h+-+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "using the quadratic formula, the roots are either:<BR>\n" );
document.write( "h = 5.16227766 or h = -1.16227766<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "since h can't be negative, the only possible answer is h = 5.16227766<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "if h = 5.16227766, then x = 1/5.16227766 = .193712943 and y = 1/7.16227766 = .13962039<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "to test this out, we substitute for x and h in the equations we created that contain h in them.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "first equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Fh%29+%2B+%281%2F%28h%2B2%29%29%29+%2A+3+=+1 ALIGN=MIDDLE  ALT=\"%28%281%2Fh%29+%2B+%281%2F%28h%2B2%29%29%29+%2A+3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "this becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2F5.16227766%29+%2B+%281%2F7.16227766%29%29+%2A+3+=+1 ALIGN=MIDDLE  ALT=\"%28%281%2F5.16227766%29+%2B+%281%2F7.16227766%29%29+%2A+3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which results in 1 = 1 proving the value of h is correct.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "second equation is x * h = 1.<BR>\n" );
document.write( "x = .193712943<BR>\n" );
document.write( "h = 5.16227766<BR>\n" );
document.write( "x * h = 1 proving the values for x and h are good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "third equation is y * (h+2) = 1.<BR>\n" );
document.write( "y = .13962039<BR>\n" );
document.write( "h + 2 = 7.16227766<BR>\n" );
document.write( "y * (h+2) = 1 proving the values for y and (h+2) are good.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "we started off with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%2By%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we then got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Ah%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%2Ah%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we then got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2A%28h%2B2%29%29+=+1 ALIGN=MIDDLE  ALT=\"%28y%2A%28h%2B2%29%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we then got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281%2Fh%29 ALIGN=MIDDLE  ALT=\"x+=+%281%2Fh%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we then got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%281%2F%28h%2B2%29%29 ALIGN=MIDDLE  ALT=\"y+=+%281%2F%28h%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we then substituted in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29+=+1 ALIGN=MIDDLE  ALT=\"%28x%2By%29+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%281%2Fh%29+%2B+%281%2F%28h%2B2%29%29%29+%2A+3+=+1 ALIGN=MIDDLE  ALT=\"%28%281%2Fh%29+%2B+%281%2F%28h%2B2%29%29%29+%2A+3+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we then solved for h.<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "once we solved for h we were then able to complete the problem.<BR>\n" );
document.write( "----- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );