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Answer :
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
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Answer:
25 minutes
Step-by-step 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.
