Question

1. which of the following equations will accurately represent the real - world situation?

a pool that holds 18,000 gallons of water is being drained at a rate of 11 gal. per minute for cleaning. how long will it take to empty the pool?
a. $0 = 11x + 18000$
b. $0 = - 11x - 18000$
c. $0 = 11x - 18000$
d. $0 = - 11x + 18000$

Explanation:

Step1: Define variables and relationship

Let $x$ = time (minutes) to drain. Remaining water = initial water - drained water. When empty, remaining water = 0.

Step2: Set up the equation

Initial water = 18000, drained water = $11x$. So $0 = 18000 - 11x$, which rearranges to $0 = -11x + 18000$.

Step3: Solve for x

Rearrange to isolate $x$:
$11x = 18000$
$x = \frac{18000}{11}$

Answer:

Equation: D. $0 = -11x + 18000$
Time to empty pool: $\frac{18000}{11} \approx 1636.36$ minutes