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)

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)

GPT-4o mini · Answer

To find out when the two vats will have an equal amount of liquid, we can set up equations for the amount of liquid in each vat over time.

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

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

For the second vat, which starts with 10 gallons and is being filled 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 have an equal amount of liquid, we can set the two expressions equal to each other: \[ 6x = 10 + 4x \]

This equation represents the point in time when both vats will contain the same amount of liquid.