Question

A bathtub containing 42 gallons of water is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Write an equation that represents the number y of gallons of water in the tub after 2 minutes.​

Answer 1

The equation representing the number of gallons of water in the tub after t minutes can be represented by a linear function y = mx + b, where y is the number of gallons of water, x is the number of minutes, m is the rate of change (or the slope) and b is the y-intercept.

Since the bathtub is draining at a constant rate, the slope (m) can be found by finding the difference between the initial number of gallons of water (42) and the number of gallons after 2 minutes (30), and dividing by the difference in time (2 minutes):

m = (42 - 30) / 2 = 6 gallons per minute

The y-intercept (b) can be found using the initial conditions of the problem, when t = 0:

b = 42 - (6 * 0) = 42

Therefore, the equation representing the number of gallons of water in the tub after t minutes can be written as:

y = 6t + 42

So, after 2 minutes, y = 6 * 2 + 42 = 54 gallons of water.

Answer 2

30.

Explanation:

We can write an equation for the number of gallons of water in the bathtub using the rate of change (drainage) and the elapsed time. Let y be the number of gallons of water in the tub after t minutes. Then, the equation can be written as:

y = 42 - (drainage rate) * t

Since we know that after 2 minutes, the tub holds 30 gallons of water, we can use this information to solve for the drainage rate:

30 = 42 - (drainage rate) * 2

12 = (drainage rate) * 2

drainage rate = 6 gallons per minute

Substituting this value into the original equation, we get:

y = 42 - 6t

So, the equation that represents the number of gallons of water in the tub after 2 minutes is:

y = 42 - 6 * 2 = 42 - 12 = 30.