If the gummy machines at a candy factory work at the same rate and six machines working simultaneously can complete a big order in 22 hours, then how many hours would it take to finish the order if the number of working machines increased by a factor of 4?
If six machines working simultaneously can complete a big order in 22 hours, then the rate at which each machine works is 1/6 of the work per hour.
If each machine works at a rate of 1/6 of the work per hour, then six machines working simultaneously complete the work at a rate of 6 * 1/6 = <<6*1/6=1>>1 work per hour.
If it took 22 hours to complete the big order, then the total work involved in the order is 22 * 1 = <<22*1=22>>22.
If the number of working machines increased by a factor of 4, then the new number of machines working simultaneously is 6 * 4 = <<6*4=24>>24 machines.
If 24 machines working simultaneously complete the work at a rate of 1 work per hour, then the new total time needed to complete the work is 22 / 24 = <<22/24=0.9166666666666666>>0.9166666666666666 hours. Answer: \boxed{0.9166666666666666}.