Question

1. peter is draining his hot tub so that he can clean it. he puts a hose in the hot tub to drain the water at a constant rate. after 5 minutes there are 430 gallons of water left in the hot tub. after 20 minutes there are 370 gallons of water left in the hot tub. let x be time (in minutes) and y be water remaining (in gallons).

equation:
use your equation to add more details to the story of peter draining the hot tub.

Explanation:

Step1: Calculate the slope (drain rate)

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Using points $(5, 430)$ and $(20, 370)$:
$m=\frac{370-430}{20-5}=\frac{-60}{15}=-4$

Step2: Find the y-intercept (initial water)

Use point-slope form $y-y_1=m(x-x_1)$ with $(5, 430)$:
$y-430=-4(x-5)$
Expand and simplify:
$y-430=-4x+20$
$y=-4x+450$

Step3: Add story details using the equation

1. Initial water: When $x=0$, $y=450$ gallons.
2. Time to empty: Set $y=0$, solve $0=-4x+450$:

$4x=450$
$x=112.5$ minutes

Answer:

Equation:

$y=-4x+450$

Added Story Details:

• Peter's hot tub started with 450 gallons of water before he began draining it.
• The hose drains the hot tub at a constant rate of 4 gallons per minute.
• It will take Peter 112.5 minutes (1 hour and 52.5 minutes) for the hot tub to completely empty so he can start cleaning.