Question

Need help on number 6

Answer 1

The equation representing the relationship between gallons in the tank and the number of hours it has been filled is g = 50h + 20.

To find the equation that represents the relationship between the amount of gallons (g) in the tank and the number of hours (h) it has been filled, we can use the information given in the table to determine the rate at which water is being pumped into the tank.

Let's denote the rate as (r) (in gallons per hour). The equation for the amount of water in the tank can be written as:

`\[ g = rh + c \]`

where:

- (g) is the amount of gallons in the tank,

- (h) is the number of hours it has been filled,

- (r) is the rate of filling (gallons per hour), and

- (c) is the initial amount of water in the tank (the amount at h = 0).

To find (r) and (c), we can use the data from the table:

1. When h = 2, g = 120.

2. When h = 5, g = 270.

Let's use these data points to find r and c:

`\[ 120 = r(2) + c \]`

`\[ 270 = r(5) + c \]`

Solve these two equations simultaneously. Subtract the first equation from the second to eliminate c:

`\[ 270 - 120 = r(5) - r(2) \]`

`\[ 150 = r(3) \]`

Now, solve for r:

`\[ r = (150)/(3) = 50 \]`

Now that we have r, substitute it back into one of the original equations to find c. Let's use the first equation:

`\[ 120 = (50)(2) + c \]`

Solve for c:

`\[ 120 = 100 + c \]`

`\[ c = 20 \]`

So, the equation that represents the relationship between the amount of gallons (g) in the tank and the number of hours (h) it has been filled is:

`\[ g = 50h + 20 \]`