Tractors

6 tractors started plowing the field that them together take 12 days.

Agronomist hesitates to

A) after 2 days to withdraw 2 tractors, or
B) after 3 days to withdraw 3 tractors.

Help him which of these two cases will be plowing done sooner.

Result




Solution:

v=1612=172  62172+4A172=1 12+4A=72 A=60/4=15 d  63172+3B172=1 18+3B=72 B=54/3=18 d  A<B   v = \dfrac{1}{6\cdot 12} = \dfrac{1}{72} \ \\ \ \\ 6 \cdot 2 \cdot \dfrac{1}{72} + 4 \cdot A \cdot \dfrac{1}{72} = 1 \ \\ 12+4A = 72 \ \\ A = 60/4 = 15 \ d \ \\ \ \\ 6 \cdot 3 \cdot \dfrac{1}{72} + 3 \cdot B \cdot \dfrac{1}{72} = 1 \ \\ 18+3B = 72 \ \\ B = 54/3 = 18 \ d \ \\ \ \\ A<B \ \\ \ \\ \ \\



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