Question 960284
rate of filling is 1/180 of the tub in one minute.
rate of emptying is 1/300 of the tub in one minute.


rate * time = quantity.
quantity is 1 full tub.
rate of filling and emptying work against each other, so their rates are subtractive.
time is what you want to find.


equation becomes:


(1/180 - 1/300) * T = 1
multiply both sides of this equation by 180 * 300 and you get:


(300 - 180) * T = 180 * 300


simplify to get:


120 * T = 180 * 300


divide both sides of this equation by 120 to get:


T = 180 * 300 / 120


simplify to get:


T = 450 minutes.


in 450 minutes, 450/180 = 2.5 times the tub has been filled and 450 / 300 = 1.5 times the tub has been emptied resulting in 1 full tub.


every minute 1/180 of the tub is being filled and 1/300 of the tub is being empties, result in a net fill of 1/450 of the tub being filled.


at that rate, the tub will be filled in 450 minutes.


the solution checks out.