Question

Adrian's backyard pool contains 6.4 gallons of water. Adrian will begin filling his pool at a rate of 4.1 gallons per second. Dale's backyard pool contains 66.4 gallons of water. Dale will begin draining his pool at a rate of 0.9 gallon per second. After how many seconds will both pools contain the same amount of water?

Answer 1

Answer:

The data that we have is:

"Adrian's backyard pool contains 6.4 gallons of water. Adrian will begin filling his pool at a rate of 4.1 gallons per second."

Then we can write the amount of water in Adrian's pool as a linear function:

A(t) = 6.4gal + (4.1gal/s)*t

Where t is our variable and represents time in seconds.

We also know that:

"Dale's backyard pool contains 66.4 gallons of water. Dale will begin draining his pool at a rate of 0.9 gallons per second. "

We can also model this with a linear function:

D(t) = 66.4 gal + (0.9gal/s)*t

Both pools will have the same amount of water when:

D(t) = A(t)

So we can find the value of t:

6.4gal + (4.1gal/s)*t = 66.4 gal + (0.9gal/s)*t

(4.1gal/s)*t - (0.9gal/s)*t = 66.4gal - 6.4gal

(3.2gal/s)*t = 60gal

t = 60gal/(3.2gal/s) = 18.75s

In 18.75 seconds both pools will have the same amount of water.