Question

A faucet delivers water at a rate of 2.7 gallons per minute. Kenny needs to fill a 30-gallon tank. The tank already has 3 gallons of water in it. Let g represent the number of gallons of water in the tank after t minutes. Write an equation that can be used to find the number of minutes, t, which it will take to fill the tank with g gallons of water. Then find the number of minutes it will take until the tank is completely full.

Answer 1

It will take 10 minutes to fill the tank completely.

Explanation:

If the 30-gallon tank already has 3 gallons of water in it, then 27 more are needed to fill the tank. Thus, at time t = 0, g(0) = 3 gallons, and

g(t) = (3 gallons) + (2.7 gal/min)t, where t is the time in minutes.

At the time the tank is completely full, it holds 30 gallons. How long does this take to achieve: Set (3 gallons) + (2.7 gal/min)t equal to 30 gallons:

30 = 3 + 2.7t, or 27 = 2.7t, or t = 10 minutes

It will take 10 minutes to fill the tank completely.