One hose can fill a small swimming pool in 90 minutes. a larger hose can fill the pool in 60 minutes. how long will it take the two hoses to fill the pool working together?

Given that one hose can fill a pool in 90 min and another can fill the pool in 60 minutes, to get how long the 2 hoses will take to fill the pool given that they are running together, we shall simply get the GCF of the times takes by the hoses, thus we shall have:

Multiples of 60 are

2,2,3,5

Multiples of 90

2,3,3,5

thus the GCF is: 2*3*5=30

Thus the two hoses working together will take 30 min