Question

A 12,000-gallon pool is being filled at a rate of 40 gallons per minute. At this rate, how many minutes will it take to fill this pool 3/4 ful

Answer 1

To fill a 12,000-gallon pool 3/4 full at a rate of 40 gallons per minute, it will take 225 minutes.

Step-by-step explanation:

To determine the time it will take to fill a 12,000-gallon pool to 3/4 full at a rate of 40 gallons per minute, we first calculate the total volume needed to reach 3/4 of the pool's capacity. We then divide it by the rate of filling to get the time in minutes.

First, find 3/4 of the 12,000-gallon capacity:

12,000 gallons × (3/4) = 9,000 gallons

This is the volume needed to fill the pool to 3/4 full.

Next, divide the volume by the rate of filling to find the time required:

9,000 gallons ÷ 40 gallons/minute = 225 minutes

Therefore, it will take 225 minutes to fill the pool 3/4 full at a rate of 40 gallons per minute.

Answer 2

Step-by-step explanation:

The first thing you have to do is find out how many gallons there will be if the pool is filled 3/4 of the way. If the pool holds 12000 gallons of water, then 3/4 of 12000 is represented in this way:

`(3)/(4)*12000` which is 9000 gallons. Now we will set up a proportion with gallons on the top and minutes on the bottom:

`(gal)/(min):(40)/(1)=(9000)/(x)`

Notice how that was set up. We kept gallons stuff on top and minutes stuff on the bottom. The x is with the minutes stuff because we want to know how many minutes, x, it will take to fill up 9000 gallons of water. This holds true as long as the rate of the flow of water remains constant. Hence, the "at this rate..." in the problem. Now we cross multiply to solve for x, the number of minutes it will take to get to 9000 gallons.

40x = 9000 so

x = 225 minutes, which is 3 hours and 45 minutes.