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

Question

as your variable. (2 points)

Answer 1

To model the situation with two pumps filling the vats, we can define an equation based on the information given:

1. Let \( x \) represent the time in minutes.

2. The first vat starts empty and is filling at a rate of 6 gallons per minute. The amount of liquid in the first vat after \( x \) minutes can be expressed as: \[ \text{Amount in first vat} = 6x \]

3. The second vat starts with 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: \[ \text{Amount in second vat} = 10 + 4x \]

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

This is the equation that shows when the two vats will have an equal amount of liquid.