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.

Plz answer

Answer 1

Let y represent the number of minutes it takes for the vats to have an equal amount of liquid.

At time x, the first vat will have a volume of 6x gallons.
At time x, the second vat will have a volume of 10 + 4x gallons.
To find the time when the two vats will have an equal amount of liquid, we set up the equation:
6x = 10 + 4x
Simplifying the equation:
6x - 4x = 10
2x = 10
Dividing both sides of the equation by 2:
x = 5
Therefore, the equation to show when the two vats will have an equal amount of liquid is:
5 minutes.

Answer 2

That is incorrect

Answer 3

Apologies for the mistake. Here is the correct equation:

Let x represent the number of minutes it takes for the vats to have an equal amount of liquid.
At time x, the first vat will have a volume of 6x gallons.
At time x, the second vat will have a volume of 10 + 4x gallons.
To find the time when the two vats will have an equal amount of liquid, we set up the equation:
6x = 10 + 4x
Subtracting 4x from both sides:
2x = 10
Dividing both sides by 2:
x = 5
Therefore, the correct equation to show when the two vats will have an equal amount of liquid is:
6x = 10 + 4x

Answer 4

To find when the two vats will have an equal amount of liquid, we can set up an equation where x represents the number of minutes it takes for the vats to have the same amount of liquid.

For the first vat, which starts empty and is being filled at a rate of 6 gallons per minute, the amount of liquid in it after x minutes can be represented as 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 it after x minutes can be represented as 10 + 4x.

We can set up the equation as follows:

6x = 10 + 4x

Simplifying the equation:

6x - 4x = 10

2x = 10

Dividing both sides of the equation by 2:

x = 5

Therefore, the two vats will have an equal amount of liquid after 5 minutes.