Answer:
[tex]h=2.564\ hours[/tex]
Step-by-step explanation:
The maximum amount of water the pool can hold is 43,000 gallons
The current amount of water is 23,000 gallons.
The filling rate is: 130 gallons per minute
This is the same as:
[tex]\frac{130\ gallons}{minute}*\frac{60\ minutes}{1\ hour} =7,800\ \frac{gallons}{hour}[/tex]
Then after one hour the amount of gallons of water will be:
[tex]7,800* 1 + 23,000[/tex]
After two hours the amount of water will be:
[tex]7,800 * 2 + 23,000[/tex]
After h hours the amount of water in the pool will be:
[tex]7,800 * h +23,000[/tex]
If we call w the amount of water in the pool then:
[tex]w=7,800h +23,000[/tex]
Now we make [tex]w = 43,000[/tex] and solve for h
[tex]7,800h +23,000=43,000[/tex]
[tex]7,800h=20,000[/tex]
[tex]h=\frac{20,000}{7,800}[/tex]
[tex]h=2.564\ hours[/tex]
