Question

Raphael begins draining oil from two different oil tanks at the same time. Tank A held 78 gallons of oil initially, and the oil is draining at a rate of 3 gallons per minute. Tank B held 122 gallons of oil initially, and the oil is draining at a rate of 5 gallons per minute.

Answer 1

Let's analyze the oil draining from both tanks.

**Tank A:**
- Initial amount of oil: 78 gallons
- Draining rate: 3 gallons per minute

We can express the amount of oil remaining in Tank A after \( t \) minutes with the following equation:
\[
\text{Amount in Tank A} = 78 - 3t
\]

**Tank B:**
- Initial amount of oil: 122 gallons
- Draining rate: 5 gallons per minute

The amount of oil remaining in Tank B after \( t \) minutes can be expressed as:
\[
\text{Amount in Tank B} = 122 - 5t
\]

### Finding the Time Until Each Tank is Empty

To find out when each tank will be empty, we can set each equation to 0.

**For Tank A:**
\[
78 - 3t = 0
\]
\[
3t = 78
\]
\[
t = \frac{78}{3} = 26 \text{ minutes}
\]

**For Tank B:**
\[
122 - 5t = 0
\]
\[
5t = 122
\]
\[
t = \frac{122}{5} = 24.4 \text{ minutes}
\]

### Summary of Results

- Tank A will be empty in **26 minutes**.
- Tank B will be empty in **24.4 minutes**.

If you need any additional information or calculations, please let me know!