a furniture manufacturer has two machines , but only one can be used at a time . machine e is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine e can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?
machine e finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of e = 5 shifts / day rate of b = 4 shifts / day rate of ( e + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / 2 ) = 13.5 shifts / day therefore , time required to finish 120 shifts = ( 120 / 13.5 ) = 8.88 . . days ~ 9 days = d
inverse(add(add(add(divide(const_1, multiply(12, const_2)), divide(divide(const_1, multiply(12, const_2)), const_2)), divide(const_1, multiply(15, const_2))), divide(divide(const_1, multiply(15, const_2)), const_2)))