A new type of pump can drain a certain pool in 8 hours. An older pump can drain the pool in 12 hours. How long will it take both pumps working together to drain the pool?

Answer 1

If first pump drains the pool in 8 hours, so it drains 1/8 of the pool in 1 hour.

I second pump drains the pool in 12 hours, so it drains 1/12 of the pool in 1 hour.

Together both pumps in 1 hour drain (1/8) + (1/12) = (3/24) + (2/24) = 5/24 of the pool.

The whole pool could be drain in 1 / (5/24) hours = 24/5 = 4 4/5 = 4.8 hours.

Answer: I twill take 4.8 hours for both pumps working together to drain the pool.

Answer 2

the new pump has work rate 1/8 pool per hour

the old pimp has work rate 1/12 pool per hour

the combined work rate is

1/8 + 1/12 = 3/24 + 2/24 = 5/24

working together, they will fill the pool in 24/5 = 4 and 4/5 hours

= 4 hours and 48 minutes