Question

Joe's Janitor Shop is getting ready for the next day's jobs. One bucket is being drained at 6 gallons per minute. The container started with 500 gallons. A second container has 200 gallons per minute and is being filled at 6 gallons per minute. How many minutes will it take for the 2 containers to have the same amount of liquid.

Answer 1

For first container

• Initial=500
• Decrease rate=-6

Equation

• y=500-6x

For second container

• Initial=200
• Increase rate=+6

Equation

• y=6x+200

Tine required for equal amount of liquid is x

• 6x+200=500-6x
• 12x=300
• x=300/12
• x=15min

Answer 2

25 minutes

Explanation:

Let x = number of minutes

Let y = amount of liquid in the bucket (in gallons)

First container

• Drained at 6 gallons per minute
• Started with 500 gallons

⇒ y = 500 - 6x

Second container

• Filled at 6 gallons per minute
• Started with 200 gallons

⇒ y = 200 + 6x

To find how many minutes it will take for the 2 containers to have the same amount of liquid, equate the equations and solve for x:

⇒ 500 - 6x = 200 + 6x

⇒ 500 - 6x + 6x = 200 + 6x + 6x

⇒ 500 = 200 + 12x

⇒ 500 - 200 = 200 - 200 + 12x

⇒ 300 = 12x

⇒ 300 ÷ 12 = 12x ÷ 12

⇒ 25 = x

⇒ x = 25

Therefore, it will take 25 minutes for the 2 containers to have the same amount of liquid.