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In a section of a timber mill, cylindrical logs of wood, all of uniform dimensions, arrive as the input and are cut into smaller cylindrical pieces of the same radius using manual and mechanical saws. To operate a manual saw four workers are needed and to operate a mechanized saw two workers are needed. The team of four workers takes two hours to cut a log into two cylindrical pieces using a manual saw, whereas just two workers are needed to do the same work in one hour using a mechanized saw. The time required to make a cut is proportional to the area across which the cut is made. How long will it take for 12 workers to cut 60 logs into four equal pieces each, if they have two mechanized saws and two manual saws?

  1. 40 hours
  2. 80 hours
  3. 120 hours
  4. 60 hours
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60 should be the correct answer.
# Since cross sectional area of any cylinder is never going to change, the time required to make a cut will always be constant for both manual and mechanical saws.
# To cut 1 log into 4 equal cylindrical pieces, we have to make 3 cuts, so to cut 60 logs each into 4 equal cylindrical pieces, we have to make 60 x 3 = 180 cuts total.

#we have sufficient man power(2 + 2 + 4 + 4) to run all the saws in parallel.

# manual saws requires time twice then time required by mechanical saws, so 1/3rd of the cuts(=60) will be made by manual saws and 2/3(= 120) will be made by mechanical saws. Thus each manual saw has to make 30 cuts and each mechanical saw has to make 60 cuts, all running in parallel.
#the time required to make 30 cuts by manual saw(2 x 30) = the time required to make 60 cuts by mechanical saw(2 x 60) = 60.

So this overall process can be done, most efficiently in 60 hours.
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