There are three pipes at the pool. The first pipe fills the pool for hours, the second pipe fills the pool for hours, and the third pipe empties the pool for hours. The janitor let the first two pipes fill the pool but after hours the second pipe stopped working. The janitor fixed the second pipe in two hours but instead of turning on the second pipe, he turned on the third pipe. He realized his mistake after one hour when he turned off the third pipe and turned on the second pipe. What is the total time needed to fill the pool?
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