SOLUTION: 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.
(a) Determine the
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(a) Determine the
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Question 1180858: 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.
(a) Determine the time the two tractors ploughing together,would take to complete the work. (3 marks)
(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.
Calculate the total time taken to plough the piece of land that day. (4 marks)
(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.
If the total work was valued at ksh 20000 , find the amount of money paid to the owner of tractor R. Found 2 solutions by ikleyn, greenestamps:Answer by ikleyn(52781) (Show Source):
I will solve part (a) ONLY, and later will explain you WHY.
The rate of work of tractor P is of the job per hour.
The rate of work of tractor Q is = of the job per hour.
Notice that represents hours = 1.6667 hours)
Their combined rate is + = of the job per hour.
It means that both tractors will complete the job in hours, or 1 hour and 15 minutes, working together. ANSWER
The other tutor answered only one question because of an unreasonable interpretation of the rule "one question per post".
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.
The other tutor also misread the information in the first part of the problem and so gave a solution to a different problem.
(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.
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.
ANSWER: 2 hours
(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 of the job in 40 minutes.
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 hours.
That's an additional 2 2/9 hours, or 2 hours 13 1/3 minutes to finish the job.
