Question

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?

Answer 1

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