SOLUTION: using 2 tractors a farmer can dig a farm in 20 days,he uses the 2 tractors for the first 8 days and added 6 more tractors to complete the work.how Long will it take to complete the

Algebra ->  Rate-of-work-word-problems -> SOLUTION: using 2 tractors a farmer can dig a farm in 20 days,he uses the 2 tractors for the first 8 days and added 6 more tractors to complete the work.how Long will it take to complete the      Log On


   

Question 1201606: using 2 tractors a farmer can dig a farm in 20 days,he uses the 2 tractors for the first 8 days and added 6 more tractors to complete the work.how Long will it take to complete the work?
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52817) About Me  (Show Source):
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.
using 2 tractors a farmer can dig a farm in 20 days. He uses the 2 tractors
for the first 8 days and added 6 more tractors to complete the work.
How long will it take to complete the work?
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                    Let' solve it MENTALLY. 


Two tractors complete the job in 20 days.

Hence, two tractors make  1%2F20  of the job per day.


Working first 8 day, two tractors made  8%2F20  of the job.

Hence,  1 - 8%2F20 = %2820-8%29%2F20 = 12%2F20  of the job remained.



    6 more added tractors make total 2+6 = 8 tractors, 
    which is 4 times as many as 2 tractors.

    Hence, 8 tractors will do  4%2F20  of the job per day.


It means that 8 tractors need  %28%2812%2F20%29%29%2F%28%284%2F20%29%29 = 12%2F4 = 3 days to complete the job.


ANSWER.  It will take 3 days to complete the job.

Solved.



Answer by josgarithmetic(39621) About Me  (Show Source):
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N%2AR%2AT=J
N workers
R rate of jobs for any one worker
T time
J number of jobs

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using 2 tractors a farmer can dig a farm in 20 days,
----------------------------------------------------

2%2Ar%2A20=1
r=1%2F40

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he uses the 2 tractors for the first 8 days and added 6 more tractors to complete the work.
------------------------------------------------------------------------------------------

Complete the Work means, finish one whole job.
First eight days, 2 tractors. Remaining time, 2+6=8 tractors.

2%2Ar%2A8%2B8%2Ar%2Ax=1
%282%2A8%29%281%2F40%29%2B8%281%2F40%29x=1
16%2B8x=40
2%2Bx=5
highlight%28x=3%29---------Three days to COMPLETE the work with the eight tractors, after the first three days with the two tractors.

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


As tutor @ikleyn indicates, you get more brain exercise, and better problem-solving experience, solving the problem using logical reasoning and simple calculations instead of formal mathematics.

Here is another informal path to a solution of the problem.

The job would have taken 20 days if he used 2 tractors for the whole time.

He used the 2 tractors for only 8 days.

After those 8 days, there would have been 12 days left if he had continued to use only 2 tractors.

But after those first 8 days he started using 2+6 = 8 tractors instead of 2.

Since he now has 4 times as many tractors, the number of days needed to complete the job gets cut by a factor of 4: the 12 days becomes 12/4 = 3 days.

ANSWER: 3 days

NOTE:
Many (most) people will say I'm too much of a stickler for proper language.... But upon reading this problem the first time I was curious how "A farmer" could use 2 tractors to do a job -- much less how he could use 8 of them....