Question 1180858
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The other tutor answered only one question because of an unreasonable interpretation of the rule "one question per post".<br>
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>
The other tutor also misread the information in the first part of the problem and so gave a solution to a different problem.<br>
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(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>
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>
ANSWER: 2 hours<br>
(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 {{{(2/3)(1/2) = 1/3}}} of the job in 40 minutes.<br>
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 {{{(2/3)/(3/10) = 20/9}}} hours.<br>
That's an additional 2 2/9 hours, or 2 hours 13 1/3 minutes to finish the job.<br>
ANSWER: 40 minutes plus 2 hours 13 1/3 minutes = 2 hours 53 1/3 minutes.<br>
(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>
P and Q together do 1/2 of the job in 1 hour. So tractor R in 1 hour does {{{5/6-1/2=1/3}}} of the job.<br>
The three tractors together finished the job in 6/5 hours, so the fraction of the job done by tractor R was {{{(6/5)(1/3)=2/5}}}.<br>
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>
ANSWER: ksh 8000<br>