Question

A bathtub has 10 gallons of water and is drained at a rate of 2 gallons every minute. Write an equation that represents the relationships between the number of gallons left in the bathtub and time.

Answer 1

The relationship between the gallons remaining in the bathtub and time is modelled by the linear equation G = 10 - 2t, where G is the gallons of water and t is the time in minutes.

Step-by-step explanation:

To solve the problem given by the student, we need to write an equation that models the relationship between the gallons of water left in the bathtub over time. Since the bathtub has 10 gallons of water and it is drained at a rate of 2 gallons per minute, we can write a linear equation to represent this situation.

Deriving the Equation

Let's denote t as the time in minutes and G as the gallons of water remaining in the bathtub. We start with 10 gallons and lose 2 gallons each minute, so the equation becomes:

G = 10 - 2t

This is a straight-line equation with a starting value (y-intercept) of 10 gallons and a slope of -2, indicating the rate at which the water level decreases.