Ryan moved into a new house with a 1750 gallon pool and needs to fill it. He can't figure out how to close his pool drain. It fills up in 1458 minutes,but it drains in 2187 1/2 minutes. When will it be full?
filling rate = 1750/1458 = 1.20 gal/min
drain rate = 1750/2187.5 = .80 gal/min
fill rate with drain open = 1.2-.8 = .4 gal/min
1750 gal/ .4 gal/min = 4375 minutes or about 73 hours
To determine when Ryan's pool will be full, we need to calculate the net rate at which the pool fills up.
Let's first find the filling rate of the pool:
The pool fills up in 1458 minutes, so the filling rate is 1 pool volume / 1458 minutes.
Next, let's find the draining rate of the pool:
The pool drains in 2187 1/2 minutes, which is equivalent to 2187.5 minutes. So, the draining rate is 1 pool volume / 2187.5 minutes.
To determine the net rate, we subtract the draining rate from the filling rate:
Net rate = filling rate - draining rate.
Now, let's calculate the net rate:
Filling rate = 1 pool volume / 1458 minutes = 1/1458 pool volume per minute.
Draining rate = 1 pool volume / 2187.5 minutes = 1/2187.5 pool volume per minute.
Net rate = 1/1458 - 1/2187.5 pool volume per minute.
Now, we can calculate the time it takes for the pool to be full by dividing the pool's volume by the net rate:
Time to fill = Pool volume / Net rate.
Pool volume = 1750 gallons.
Substituting the pool volume and the net rate into the equation:
Time to fill = 1750 / (1/1458 - 1/2187.5).
Let's simplify the equation:
Time to fill = 1750 / [(2187.5 - 1458) / (1458 * 2187.5)].
Simplifying further:
Time to fill = 1750 / (729 / (1458 * 2187.5)).
Time to fill = 1750 / (729 / 3188647.5).
Time to fill = 1750 * 3188647.5 / 729.
Time to fill = 7633425000 / 729.
Time to fill = 10485700.
Therefore, it will take approximately 10,485,700 minutes for Ryan's pool to be full.