Two pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 galions 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 z as your variable. (1 point)

Answer 1

To write an equation showing when the two vats will have an equal amount of liquid, we first need to define the amounts of liquid in each vat.

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

2. The first vat starts empty and is being filled at a rate of 6 gallons per minute. Therefore, the amount of liquid in the first vat after \( z \) minutes is: \[ 6z \]

3. The second vat starts with 10 gallons and is being filled at a rate of 4 gallons per minute. Therefore, the amount of liquid in the second vat after \( z \) minutes is: \[ 10 + 4z \]

To find out when both vats have the same amount of liquid, we set the two expressions equal to each other: \[ 6z = 10 + 4z \]

This equation can be solved for \( z \) to find the time when both vats contain the same amount of liquid.