The new type of pump and the old pump working together will drain the pool in 4 hours and 57 minutes.
The new type of pump drains the pool in 9 hours.
So, the new type of pump will drain 1/9 of the pool each hour.
The old pump drains the pool in 11 hours.
The old pump will drain 1/11 of the pool each hour.
Now, when both the pumps are working together:
The two pumps will drain 1/9 + 1/11 = ( 11 + 9) / 99 = 20/99 of the pump volume per hour.
Therefore,
It will take 99/20 hours = 4 19/20 hours
4 19/20 hours = 4.95 hours which is equal to 4 hours 57 minutes for two pumps working together to drain the pool.
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