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.

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.

Note: The answer Isn't 5

Answer 1

Let's assume that after x minutes, the empty vat will have an equal amount of liquid as the filled vat.

After x minutes, the empty vat will have 6x gallons of liquid.

The filled vat already has 10 gallons and is filling at a rate of 4 gallons per minute, so it will have 10 + 4x gallons after x minutes.

Now, to set up the equation:

6x = 10 + 4x

Subtract 4x from both sides:

2x = 10

Divide both sides by 2:

x = 5

So, the equation that represents when the two vats will have an equal amount of liquid is 6x = 10 + 4x.