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.

3 answers

Let V represent the amount of liquid in the empty vat and t represent the time in minutes.

The rate at which the empty vat is filling is 6 gallons per minute. Therefore, the amount of liquid in the empty vat is given by the equation:

V = 6t

The rate at which the other vat is filling is 4 gallons per minute, and it already contains 10 gallons of liquid. Therefore, the amount of liquid in the other vat is given by the equation:

V = 4t + 10

Since we want to find when the two vats will have an equal amount of liquid, we set the two equations equal to each other:

6t = 4t + 10

Subtract 4t from both sides:

2t = 10

Finally, divide both sides by 2:

t = 5

So, the two vats will have an equal amount of liquid after 5 minutes.
wrong
Apologies for the mistake. Let's correct the equation.

Let V represent the amount of liquid in the empty vat and t represent the time in minutes.

The rate at which the empty vat is filling is 6 gallons per minute. Therefore, the amount of liquid in the empty vat is given by the equation:

V = 6t

The rate at which the other vat is filling is 4 gallons per minute, and it already contains 10 gallons of liquid. Therefore, the amount of liquid in the other vat is given by the equation:

V = 4t + 10

To find the time t at which the two vats will have an equal amount of liquid, we set the two equations equal to each other:

6t = 4t + 10

Subtract 4t from both sides:

2t = 10

Finally, divide both sides by 2:

t = 5

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