A water tank initially contained 108 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute.How many minutes have passed, m, when the tank contains 178 liters? Round to the nearest hundredth.

We are given that the water tank initially contains 108 liters of water. Water is added at a constant rate of 9 liters per minute. We are asked to find the number of minutes, \(m\), when the tank contains 178 liters.

### Step-by-step process:

1. **Initial amount of water in the tank**: 108 liters.
2. **Rate of water being added**: 9 liters per minute.
3. **Final amount of water in the tank**: 178 liters.

To find the time \(m\), we can set up the equation:

\[
\text{Amount of water after } m \text{ minutes} = 108 + 9m
\]

We know the final amount is 178 liters, so:

\[
178 = 108 + 9m
\]

### Solving for \(m\):
1. Subtract 108 from both sides:
   \[
   178 - 108 = 9m
   \]
   \[
   70 = 9m
   \]

2. Divide both sides by 9:
   \[
   m = \frac{70}{9} \approx 7.78
   \]

Thus, the number of minutes that have passed is approximately \(m \approx 7.78\).

Would you like a further explanation or have any questions?

Here are five follow-up questions to think about:
1. What if the tank started with a different amount of water, say 50 liters?
2. How would the answer change if water were added at 12 liters per minute instead of 9?
3. What would be the total amount of water after 15 minutes?
4. Can you write a general formula to determine the time \(m\) for any initial and final water amounts?
5. What if instead of being filled, water was being drained at a constant rate?

**Tip:** When solving for a variable, always perform inverse operations (e.g., addition → subtraction, multiplication → division) to isolate the variable.

A water tank initially contained 108 liters of water. It is then filled with more water, at a constant rate of 9 liters per minute. How many minutes have passed, m, when the tank contains 178 liters? Round to the nearest hundredth.

Learn how to solve a linear equation involving a water tank filled at a constant rate of 9 liters per minute. The problem starts with 108 liters and calculates how long it takes to reach 178 liters. Detailed solution included, suitable for Grade 7-8 students.

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