QuestionA 28,000-gallon pool drains at 700 gallons/hour. What equation relates gallons left ( $g$ ) to time ( $t$ )? $g=28,000-700 t$

Studdy Solution

STEP 1

Assumptions1. The initial volume of the pool is28,000 gallons. The pump drains the pool at a constant rate of700 gallons per hour3. $g$ represents the number of gallons remaining in the pool4. $t$ represents the time in hours the pool has been draining

STEP 2

We need to find an equation that models this situation. Since the pump is draining the pool, the number of gallons in the pool is decreasing over time. This means that as time goes on (as $t$ increases), the number of gallons remaining in the pool ( $g$ ) decreases.

STEP 3

We start with the initial volume of the pool (28,000 gallons) and subtract the amount of water that the pump drains each hour (700 gallons per hour times the number of hours $t$ ). This gives us the number of gallons remaining in the pool after $t$ hours.
$g = Initial\, volume - (Drain\, rate \\times Time)$

STEP 4

Now, plug in the given values for the initial volume and drain rate to form the equation.
$g =28,000 - (700 \\times t)$ So, the equation that models this situation is $g =28,000 -700t$ This equation tells us that the number of gallons remaining in the pool ( $g$ ) is equal to the initial volume of the pool (28,000 gallons) minus the total amount of water drained by the pump (700 gallons per hour times the number of hours $t$ ).

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