Certainly! Let's work through the question step-by-step.
### Step 1: Understanding the Problem
We start with a tank that has 400 liters (L) of water. Water is being emptied from the tank at a constant rate of 32 liters per minute (L/min). We want to determine how long it will take until the tank contains only 112 liters of water.
### Step 2: Set Up the Problem
Let [tex]\( t \)[/tex] be the time in minutes it takes to reduce the water level in the tank to 112 liters.
### Step 3: Formulate the Equation
We can create an equation based on the rate of emptying and the initial and final water levels. The amount of water left in the tank after [tex]\( t \)[/tex] minutes is given by the initial amount of water minus the amount emptied.
[tex]\[ \text{Initial water} - (\text{rate of emptying} \times \text{time}) = \text{final water} \][/tex]
Using the numbers provided:
[tex]\[ 400 \, \text{L} - (32 \, \text{L/min} \times t) = 112 \, \text{L} \][/tex]
### Step 4: Solve the Equation for [tex]\( t \)[/tex]
First, isolate [tex]\( t \)[/tex] on one side of the equation:
[tex]\[ 400 - 32t = 112 \][/tex]
Subtract 112 from both sides to simplify:
[tex]\[ 400 - 112 = 32t \][/tex]
[tex]\[ 288 = 32t \][/tex]
Now, solve for [tex]\( t \)[/tex] by dividing both sides by 32:
[tex]\[ t = \frac{288}{32} = 9 \][/tex]
So, [tex]\( t = 9 \)[/tex] minutes.
### Step 5: Round the Answer
Since our calculated [tex]\( t \)[/tex] is exactly 9, there's no need to round. The nearest whole number is 9.
### Conclusion
It will take approximately 9 minutes to reduce the amount of water in the tank from 400 liters to 112 liters.
