A swimming pool can be filled by one pump in 5.1 hours and by another pump in 3 hours and 50 minutes. If the first pump starts operating, after the second pumps worked 1.5 hours, how long will it take the two pumps to fill in the pool full together?

1.332 hours

Step-by-step explanation:

Assume the swimming pool has a volume V [L],

The rate of the first pump is = V / 5.1 = 0.1961V [L/h]

3 hours and 50 minutes = 3 + 50/60 = 3.833

The rate of the second pump is = V / 3.833 = 0.2609V [L/h]

After the second pump has worked 1.5 hours it has filled:

Volume filled = 0.2609V * 1.5 = 0.39135V

The 2 pumps needs to fill the remaining volume:

Remaining volume = V - 0.39135V = 0.60865V

And the rate of both pumps together is:

0.1961V + 0.2609V = 0.457V

The time needed to fill the remaining volume is:

Time = 0.60865V / 0.457V = 1.332 hours