Pool filling up

Question

Mike and his sister want to go swimming in their new pool. However, first they need to fill it with water. It takes one hose 24 hours to fill the pool; it takes another hose 16 hours to fill the pool. How long will it take to fill the pool if both hoses are running at the same time?

Answer 1

1 hose takes 24 hours alone so it does 1/24 of the pool per hour

1 hose takes 16 hours alone so it does 1/16 of the pool per hour

 

(1/24+1/16)(x hours) = 100%

x(2/48 + 3/48) = 1

x(5/48) = 1

x = 1/(5/48)

x = 48/5 = 9 3/5 hours

 

If you need the answer in hours and minutes:

3/5 hours = (3/5 hrs)(60 min/hr) = 36 mins

So the time is 9 hours 36 minutes

 

Hope this helps.  Good luck