A 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour. Which equation models this situation if g is the number of gallons remaining in the pool and t is the amount of time in hours the pool has been draining?

Answer 1

To model the situation where a 28,000-gallon swimming pool is being drained at a rate of 700 gallons per hour, we can use a linear equation to represent the number of gallons remaining in the pool, \( g \), after \( t \) hours of draining.

Initially, the pool contains 28,000 gallons. Each hour, 700 gallons are removed. Therefore, the number of gallons remaining in the pool decreases by 700 gallons every hour.

We start with the following details:
- Initial volume of the pool: 28,000 gallons.
- Rate at which the pool is being drained: 700 gallons per hour.

The equation that models the volume of water remaining in the pool after \( t \) hours of draining is:
\[ g = 28000 - 700t \]

Here:
- \( g \) is the number of gallons remaining in the pool.
- \( t \) is the number of hours the pool has been draining.

This linear equation accurately represents the relationship between the gallons remaining and the time elapsed while draining the pool.