# Pump 1 can empty a pool in 8 hours while Pump 2 can empty the same pool in 9 hours. If the two pumps worked together, how long would it take them to empty the pool?

QUESTION POSTED AT 29/05/2020 - 04:50 PM

QUESTION POSTED AT 29/05/2020 - 04:50 PM

Rate of pump A: 1/8 of a pool per hour

Rate of pump B: 1/9 of a pool per hour

Combined rate: 1/8+1/9 = 17/72 +1/9 = 25/72

So if they work together, the two pumps have a combined rate of 25/72 of a pool per hour (i.e in one hour, the two pumps will empty 25/72 of the pool)

But we want to empty ONE pool (not 25/72 of one). So we need to multiply 25/72 by some number x to get 1.

Now solve for x

x=2.88

It will take the two pumps 2.88 hours to empty the pool.

2 hours 52 minutes 50 seconds

Rate of pump B: 1/9 of a pool per hour

Combined rate: 1/8+1/9 = 17/72 +1/9 = 25/72

So if they work together, the two pumps have a combined rate of 25/72 of a pool per hour (i.e in one hour, the two pumps will empty 25/72 of the pool)

But we want to empty ONE pool (not 25/72 of one). So we need to multiply 25/72 by some number x to get 1.

Now solve for x

x=2.88

It will take the two pumps 2.88 hours to empty the pool.

2 hours 52 minutes 50 seconds

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