Afactory is currently running at 85% of its original capacity, and management is considering upgrading the equipment.

the upgrade will take 6 months, during which time the factory will not run at all. once complete, the factory’s output will increase to 120% of the original capacity. after how long would the upgraded factory’s production match the current 85% production? in other words, how long will it take for the factory to make up for the loss of 6 months?

(hint: the problem can be solved using a system of equations, but any method is acceptable as long as it is justified. if you get stuck, try letting the factory’s original output be 100 units per month.)

serious answers only. i would appreciate work shown!