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 34 full?

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:

which is 9000 gallons. Now we will set up a proportion with gallons on the top and minutes on the bottom:

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.

Step-by-step explanation:

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