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Lisa [10]
2 years ago
5

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.
Mathematics
2 answers:
shusha [124]2 years ago
4 0

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
posledela2 years ago
3 0

Answer:

25 minutes

Step-by-step explanation:

Let x = number of minutes

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

<u>First container</u>

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

⇒ y = 500 - 6x

<u>Second container</u>

  • 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 <u>25 minutes</u> for the 2 containers to have the same amount of liquid.

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