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

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): You can put this solution on YOUR website!
.

            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

Solved.

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It is a standard and typical joint work problem.

There is a wide variety of similar solved joint-work problems with detailed explanations in this site. See the lessons
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    - Solving more complicated word problems on joint work
    - Selected joint-work word problems from the archive

Read them and get be trained in solving joint-work problems.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook under the topic
"Rate of work and joint work problems" of the section "Word problems".

Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

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.

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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.

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.

ANSWER: 40 minutes plus 2 hours 13 1/3 minutes = 2 hours 53 1/3 minutes.

(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.

P and Q together do 1/2 of the job in 1 hour. So tractor R in 1 hour does of the job.

The three tractors together finished the job in 6/5 hours, so the fraction of the job done by tractor R was .

So the amount to be paid to the owner of tractor R is 2/5 of the total of ksh 20000, or ksh 8000.

ANSWER: ksh 8000

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