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!