Linear Equations in Real-World Scenarios Practice

Question

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Question
Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other is already filled with 10 gallons, and it is continuing to fill at a rate of 4 gallons per minute. Write an equation to show when the two vats will have an equal amount of liquid. Use x
as your variable. (2 points)

Remaining Attempts 1

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Answer 1

To solve the problem, we need to set up equations for the amount of liquid in each vat over time.

Let \( x \) represent the number of minutes that have passed.

• For the first vat (initially empty and filling at 6 gallons per minute): \[ \text{Amount in First Vat} = 6x \]

• For the second vat (initially filled with 10 gallons and filling at 4 gallons per minute): \[ \text{Amount in Second Vat} = 10 + 4x \]

We want to find when the amounts in both vats are equal: \[ 6x = 10 + 4x \]

Thus, the equation showing when the two vats will have an equal amount of liquid is: \[ 6x = 10 + 4x \]

You can input it in the format provided: \[ 6x = 10 + 4x \]