To find the time when the two vats will have an equal amount of liquid, we need to set up an equation. Let's denote the time in minutes as x.
The rate at which the first vat is being filled is 6 gallons per minute. Therefore, the amount of liquid in the first vat after x minutes is 6x gallons.
The rate at which the second vat is being filled is 4 gallons per minute. Since the second vat already has 10 gallons, the amount of liquid in the second vat after x minutes is 10 + 4x gallons.
To find the time when the two vats will have an equal amount of liquid, we set the two expressions equal to each other:
6x = 10 + 4x
Now, we can solve for x. Subtract 4x from both sides:
6x - 4x = 10
Simplifying the equation, we have:
2x = 10
Finally, divide both sides by 2:
x = 5
So, the two vats will have an equal amount of liquid after 5 minutes.