Question

Water is draining out of an 800-gallon hot tub. The water is draining at a rate of 20 gallons per minute. At time t = 0 minutes, the tub starts draining. Use the values in this problem to complete the inequality to represent the time [t] when the volume of water in the tub is less than or equal to 640 gallons.

Answer 1

The time [t] when the volume of water in the tub is less than or equal to 640 gallons is t ≥ 8 minutes. Therefore, the time [t] when the volume of water in the tub is less than or equal to 640 gallons is t ≥ 8 minutes.

Step-by-step explanation:

To find the time [t] when the volume of water in the tub is less than or equal to 640 gallons, we can use the equation:

Volume of water in tub = Initial volume - Drainage rate x Time

Since the initial volume is 800 gallons and the drainage rate is 20 gallons per minute, the inequality can be written as:

800 - 20t ≤ 640

Simplifying the inequality, we have:

-20t ≤ -160

Dividing both sides by -20, we get:

t ≥ 8

Therefore, the time [t] when the volume of water in the tub is less than or equal to 640 gallons is t ≥ 8 minutes.