Two tractors working together cultivated 2 3 of a field in 4 days. how long would it take each tractor to cultivate the whole field by itself if the first tractor can do the job 5 days faster than the second?

Let the time for the 1st tractor alone be A, and the time for the 2nd tractor alone be B. Then in 1 day, the 1st tractor does 1/A, and the 2nd does 1/B. Together, both complete 2/3 of the field in 4 days:

(1/A + 1/B) (4 days) = 2/3

1/A + 1/B = 1/6

If the 1st tractor can finish in 5 days less than the 2nd:

A = B - 5

Substituting:

1 / (B - 5) + 1/B = 1/6

(2B - 5) / B (B - 5) = 1/6

6 (2B - 5) = B (B - 5)

12B - 30 = B^2 - 5B

B^2 - 17B - 30 = 0

(B - 15) (B - 2) = 0

B = 15 (B = 2 is extraneous since A would then be - 3)

A = B - 5 = 10

Therefore, the 1st tractor would take 10 days, and the 2nd would take 15.