Question

TANK A large tank is currently holding 12,000 gallons of water. The water will drain at a constant rate of 100 gallons per minute until the volume of water in the tank is 4,000 gallons. Write an equation to find the number of minutes m it will take for the specified amount of water to drain.

Answer 1

To find the number of minutes \( m \) it will take for the water in Tank A to drain from 12,000 gallons to 4,000 gallons at a constant rate of 100 gallons per minute, you can set up the following equation:

1. Determine the total amount of water that needs to be drained:
\[
\text{Water to drain} = 12,000 \text{ gallons} - 4,000 \text{ gallons} = 8,000 \text{ gallons}
\]

2. Since the water is draining at a rate of 100 gallons per minute, you can express the time in minutes \( m \) to drain this amount using the equation:
\[
\text{Water drained} = \text{drain rate} \times m
\]
Substituting the known values:
\[
8,000 = 100 \times m
\]

3. To solve for \( m \), divide both sides by 100:
\[
m = \frac{8,000}{100} = 80
\]

So, the number of minutes it will take for the specified amount of water to drain is \( m = 80 \) minutes.

In summary, the equation to find \( m \) is:
\[
m = \frac{12,000 - 4,000}{100}
\]