document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=767200>Question 767200</A>: <I><SPAN STYLE=\"word-break: break-all;\">  John is being paid $864 to do a landscape job. It took him 6 hours less than he expected, so he earned $2 per hour more than he originally calculated. How long had he anticipated it would take to do the landscaping?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #467484 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=467484\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let h = number of hours originally costed<BR>\n" );
document.write( "Let r = the rate at which the h hours were costed.<BR>\n" );
document.write( "Then we have<BR>\n" );
document.write( "(1) r*h = 864 or<BR>\n" );
document.write( "(2) h = 864/r<BR>\n" );
document.write( "When he finished he was paid $864 as he charged them, but he took 6 hours less which in effect increased the hourly rate r. In the end his pay was<BR>\n" );
document.write( "(3) (r+2)*(h-6) = 864<BR>\n" );
document.write( "Equating (1) and (3) we get<BR>\n" );
document.write( "(4)(r+2)*(h-6) = r*h or after FOILing gives us<BR>\n" );
document.write( "(5) r*h - 6r + 2h - 12 = r*h or<BR>\n" );
document.write( "(6) 2h = 12 + 6r or<BR>\n" );
document.write( "(7) h = 6 +3r<BR>\n" );
document.write( "Now equate (7) and (2) to get<BR>\n" );
document.write( "(8) 3r + 6 = 864/r or after multiplying by r we get<BR>\n" );
document.write( "(9) 3r^2 + 6r - 864 = 0 or after dividing by 3 we get<BR>\n" );
document.write( "(10) r^2 + 2r - 288 = 0 which factors into <BR>\n" );
document.write( "(11) (r + 18)*(r - 16) = 0<BR>\n" );
document.write( "Taking the positive root gives us<BR>\n" );
document.write( "(12) r = 16<BR>\n" );
document.write( "Use (12) in (2) gives us<BR>\n" );
document.write( "(13) h = 54<BR>\n" );
document.write( "Let's check this with (1)<BR>\n" );
document.write( "Is (16*54 = 864)?<BR>\n" );
document.write( "Is (864 = 864)? Yes<BR>\n" );
document.write( "Then after the job was finished he spent 54-6 or 48 hours on the job. He said that was, in effect, his original rate plus $2. Let's check this with (3).<BR>\n" );
document.write( "Is ((16+2)*(54-6) = 864)?<BR>\n" );
document.write( "Is (18*48 = 864)?<BR>\n" );
document.write( "Is( 864 = 864)? Yes<BR>\n" );
document.write( "Answer: He originally anticipated that it would take 54 hours to do the landscaping job. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );