An aquifer receives $20 m^3$ of precipitation and loses $2 m^3$ of water through natural movement. If the water budget must be balanced, how much water can be pumped from the aquifer?
A. $22 m^3$
B. $36 m^3$
C. $18 m^3$
D. $20 m^3
Answer (1)
Define variables: P (precipitation), L (water loss), and W (water pumped).
Set up the balanced water budget equation: P = L + W .
Substitute given values: 20 = 2 + W .
Solve for W : W = 18 . The amount of water that can be pumped is 18 m 3 .
Explanation
Understanding the Problem We are given that an aquifer receives 20 m 3 of precipitation and loses 2 m 3 of water through natural movement. We need to find out how much water can be pumped from the aquifer if the water budget must be balanced.
Setting up the Equation Let P be the amount of precipitation received by the aquifer, L be the amount of water lost through natural movement, and W be the amount of water that can be pumped from the aquifer. The water budget is balanced when the amount of water entering the aquifer equals the amount of water leaving the aquifer. This can be represented by the equation: P = L + W
Substituting the Values We are given P = 20 m 3 and L = 2 m 3 . Substituting these values into the equation, we get: 20 = 2 + W
Solving for W Now, we solve for W :
W = 20 − 2 W = 18 Therefore, 18 m 3 of water can be pumped from the aquifer.
Final Answer The amount of water that can be pumped from the aquifer while maintaining a balanced water budget is 18 m 3 .
Examples
Imagine you are managing a city's water resources. The aquifer is like a savings account for water. Precipitation is like deposits, and natural water movement and pumping are like withdrawals. To ensure the city has enough water, you need to balance the deposits and withdrawals. This problem helps you calculate how much water you can safely pump (withdraw) without depleting the aquifer (savings account). This ensures a sustainable water supply for the city.
