Remember that all data should be expressed either in cubic feet or gallons. Choose one of these measurements and express all numbers in terms of it.
1 hour and 40 minutes
Practice makes perfect
Let's start with writing the equation in point-slope form and then use it to determine how long it will take to fill the pool completely.
Write The Equation
In order to write the equation in point-slope form, we need to know the slope and a point that lies on the line. We are told that water is being added to the pool at a rate of about 20 cubic feet per minute. Since slope represents a constant rate of change, we can conclude that m= 20.
y-y_1= 20(x-x_1)We are also given that, when 0 minutes had passed, there was already 1200 gallons of water. Notice, some numbers are expressed in cubic feet and some in gallons. Let's agree to express all measurements in cubic feet. Since 1 cubic foot of space holds 7.5 gallons of water, we can rewrite 1200 gallons in cubic feet by dividing by 7.5.
1200/7.5=160 cubic feet
Now we can write the point, which is a solution to the equation, as ( 0, 160). Let's substitute it into the equation for this situation.
y- 160=20(x- 0) ⇔ y-160=20x
Calculate The Time
We are told that the swimming pool has a volume capacity of 2160 cubic feet. Therefore, to determine how long it will take to fill the pool completely, let's substitute y with 2160 and solve for x.
