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

A. [tex]\( 28,000 = -700t \)[/tex]
B. [tex]\( 28,000g = -700t \)[/tex]
C. [tex]\( g = 700t - 28,000 \)[/tex]
D. [tex]\( g = 28,000 - 700t \)[/tex]



Answer :

To determine the equation that models the situation where a 28,000-gallon swimming pool is being drained using a pump that empties 700 gallons per hour, we need to analyze the given information step by step.

1. Initial Amount: The pool starts with 28,000 gallons of water. This is our initial condition before any drainage occurs.

2. Rate of Drainage: The pool is losing water at a rate of 700 gallons per hour. This means every hour, 700 gallons of water are removed from the pool.

3. Variables:
- [tex]\( g \)[/tex] represents the number of gallons of water remaining in the pool.
- [tex]\( t \)[/tex] represents the number of hours the pool has been draining.

4. Change in Water Volume: After [tex]\( t \)[/tex] hours, the total amount of water drained from the pool is [tex]\( 700 \times t \)[/tex] gallons. This is because the rate of 700 gallons per hour times the number of hours [tex]\( t \)[/tex] gives the total amount of water drained.

5. Remaining Water: To find the remaining water in the pool after [tex]\( t \)[/tex] hours, we subtract the drained water from the initial amount of 28,000 gallons.

Putting this all together, we can write the equation for the remaining water [tex]\( g \)[/tex] as follows:

[tex]\[ g = 28000 - 700 \times t \][/tex]

Therefore, the correct equation that models the number of gallons remaining in the pool after [tex]\( t \)[/tex] hours of draining is:

[tex]\[ g = 28000 - 700 \times t \][/tex]

So, out of the given options, the correct choice is:

[tex]\[ g = 28000 - 700 t \][/tex]