Aa P.

asked • 10/03/19

multiple mowers working together

I have 4 mowers and 30 sqmi to mow. how do I optimize how many sqmi each mower has to mow to finish within 50 hours

mower 1 2.23hr/sqmi

mower 2 1.43hr/sqmi

mower 3 5.52hr/sqmi

mower 4 2.95hr/sqmi

Aa P.

Or if unable to finish in 50 hours how many sqmi each mower will do to finish in the fastest possible time
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10/03/19

Heidi T.

If you have 50 hours, then Mower 2 can finish the job by itself in 42.9 hours. Time to mow = rate (hr/mi^2) * (#sq mi) = (1.43 hr/mi^2)*(30 mi^2) = 42.9 hours. If you want to finish in the shortest possible time period with all 4 mowers working at the same time, with the combined time of operation adding to 50 hours, it's a totally different problem.
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10/03/19

1 Expert Answer

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Mark M. answered • 10/03/19

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Time needed working alone

1) 66.9

2) 42.9

3) 165.6

4) 88.5


t represents the time working together.


(t / 66.9) + (t / 42.9) + (t / 165.6) + (t / 88.5) = 1

628725.24t + 980459.64t + 253995.885t + 475273.656t = 42061718.56

2338454.421t = 42061718.56

t = 17.98697387


Working together the mowers would need slightly less than 18 hours.

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