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Two pumps are available to fill a swimming pool. The larger pump can fill the pool in 8 hours if it works alone. The smaller pump would take 17 hours to fill the pool it it worked by itself. The large pump was busy on another job so the pool superintendent began to fill the pool with the smaller pump. Seven hours after the small pump began to fill the pool, the larger pump arrived and began to work along with the smaller pump. How long was the larger pump working when the pool was full? How long had the smaller pump been working?
The larger pump fills 1/8 the pool in 1 hour
The smaller pump fills 1/17 pool in 1 hour
They both together fill 1/8 +1/17 of the pool in 1 hour= 25/136 of the pool
small pump worked for 7 hours alone.
So it had filled up 1/17*7 of the pool = 7/17 of the pool
Balance remaining after 7 hours will be 1-7/17 of the pool = 10/17
Both together fill 25/136 of the pool in 1 hour
So to fill up the balance10/17 of the pool they will take 10/17 / 25/136 = 3.2 hours
The larger pump worked for 3.2 hours
The smaller pump worked for 7+3.2 = 10.2 hours