Final answer:
The equation representing the situation of the rainwater level increase is 40 inches + (4 * r) = 52 inches. By solving this equation, we find that the rate of rainfall each day (r) is 3 inches per day.
Step-by-step explanation:
The situation described can be represented by an equation using the variable r for the rate of rainfall each day. The rainwater collection tank initially contained 40 inches and increased to 52 inches over 4 days. To find the daily rain rate, let's denote the rise in water level as the result of 4 days of rain at a consistent rate r.
The total increase in water levels is 52 inches - 40 inches = 12 inches over 4 days. Thus, the equation that represents this situation is:
40 inches + (4 days * r) = 52 inches.
Now, solving for r, we get:
4r = 52 inches - 40 inches
4r = 12 inches
r = 12 inches / 4 days
r = 3 inches/day
So, the rate of rainfall each day is 3 inches.