document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1180858>Question 1180858</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A farmer has two tractors P and Q. Tractor P, working alone, can plough a piece of land in 5 hours while tractor Q would take 1.6667 hours less than tractor P.<BR>\n" );
document.write( " (a) Determine the time the two tractors ploughing together,would take to complete the work. (3 marks) <BR>\n" );
document.write( "(b) One day, the tractors started to plough the piece of land together. After 40 minutes,tractor P broke down but Q continued alone and completed the work.<BR>\n" );
document.write( "Calculate the total time taken to plough the piece of land that day. (4 marks) <BR>\n" );
document.write( "(c) In another season, the farmer hired an additional tractor R to assist P and Q which retained the same rate of working as before. The three tractors took I hour 12 minutes to plough the same piece of land. The owner of tractor R was paid some money proportional to the work done by the tractor.<BR>\n" );
document.write( "If the total work was valued at ksh 20000 , find the amount of money paid to the owner of tractor R. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #810669 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=810669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor answered only one question because of an unreasonable interpretation of the rule \"one question per post\".<br><BR>\n" );
document.write( "Your post is not several separate unrelated questions; it is a single problem with three related questions.  Posting the three questions as separate posts would make no sense; they NEED TO BE posted together.<br><BR>\n" );
document.write( "The other tutor also misread the information in the first part of the problem and so gave a solution to a different problem.<br><BR>\n" );
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document.write( "(a) Tractor P can do the job alone in 5 hours; tractor Q can do it in (5-1.6667)=3.333 hours.  So P can do (1/5) of the job in 1 hour and Q can do (1/3.333) = 3/10 of the job in 1 hour.<br><BR>\n" );
document.write( "Working together then, the two tractors can do 1/5+3/10 = 1/2 of the job in 1 hour; so they can do the job together is 1/(1/2) = 2 hours.<br><BR>\n" );
document.write( "ANSWER: 2 hours<br><BR>\n" );
document.write( "(b) P and Q work together for 40 minutes (2/3 of an hour).  Since together they can do 1/2 of the job in one hour, they do <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%281%2F2%29+=+1%2F3 ALIGN=MIDDLE  ALT=\"%282%2F3%29%281%2F2%29+=+1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job in 40 minutes.<br><BR>\n" );
document.write( "So 2/3 of the job remains to be done.  The additional time it takes Q to finish the job, working at 3/10 of the job per hour, is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%2F%283%2F10%29+=+20%2F9 ALIGN=MIDDLE  ALT=\"%282%2F3%29%2F%283%2F10%29+=+20%2F9\"   DISABLED_style= \"max-width:90%; height:auto;\" > hours.<br><BR>\n" );
document.write( "That's an additional 2 2/9 hours, or 2 hours 13 1/3 minutes to finish the job.<br><BR>\n" );
document.write( "ANSWER: 40 minutes plus 2 hours 13 1/3 minutes = 2 hours 53 1/3 minutes.<br><BR>\n" );
document.write( "(c) The three tractors together take 1 hour 12 minutes to finish the job together, or 6/5 hours.  That means they do 5/6 of the job together in 1 hour.<br><BR>\n" );
document.write( "P and Q together do 1/2 of the job in 1 hour. So tractor R in 1 hour does <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F6-1%2F2=1%2F3 ALIGN=MIDDLE  ALT=\"5%2F6-1%2F2=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the job.<br><BR>\n" );
document.write( "The three tractors together finished the job in 6/5 hours, so the fraction of the job done by tractor R was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F5%29%281%2F3%29=2%2F5 ALIGN=MIDDLE  ALT=\"%286%2F5%29%281%2F3%29=2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "So the amount to be paid to the owner of tractor R is 2/5 of the total of ksh 20000, or ksh 8000.<br><BR>\n" );
document.write( "ANSWER: ksh 8000<br><BR>\n" );
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