Question

jamal is draining his pool for the winter.

• after 30 minutes, there are 12,750 gallons in the pool
• after 90 minutes, there are 11,250 gallons in the pool

derek has a smaller pool and the number of gallons in his pool can be represented by the equation ( y = -20x + 10,700 ). whose pool is draining at a slower rate and by how much?
s pool is draining at a slower rate by

Explanation:

Step1: Find Jamal's draining rate

Jamal's pool: at \( x = 30 \) minutes, \( y = 12750 \) gallons; at \( x = 90 \) minutes, \( y = 11250 \) gallons.
The rate of change (draining rate) is slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{11250 - 12750}{90 - 30}=\frac{-1500}{60}=-25 \) gallons per minute.

Step2: Find Derek's draining rate

Derek's equation: \( y=-20x + 10700 \). The slope (draining rate) is \( -20 \) gallons per minute.

Step3: Compare the rates

Jamal's rate: \( 25 \) gallons/min (magnitude), Derek's rate: \( 20 \) gallons/min.
Difference: \( 25 - 20 = 5 \) gallons per minute.

Answer:

Derek's pool is draining at a slower rate by 5 gallons per minute.