Question

Linear Equations in Real-World Scenarios Practice
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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. (1 point)

Answer 1

Let's denote \( x \) as the number of minutes that have passed.

For the first vat, which is empty and filling at a rate of 6 gallons per minute:
- The amount of liquid in the first vat after \( x \) minutes can be expressed as:
\[ A_1 = 6x \]

For the second vat, which already has 10 gallons and is filling at a rate of 4 gallons per minute:
- The amount of liquid in the second vat after \( x \) minutes can be expressed as:
\[ A_2 = 10 + 4x \]

To find the time when both vats will have an equal amount of liquid, we can set the two equations equal to each other:
\[ 6x = 10 + 4x \]

This equation represents the point at which both vats are filled to the same level.