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. (1 point)

Answer 1

To find out when the two vats will have an equal amount of liquid, we can set up equations for the amount of liquid in each vat over time.

Let \( x \) represent the time in minutes.

For the first vat, which starts empty and is being filled at a rate of 6 gallons per minute, the amount of liquid in the first vat after \( x \) minutes can be expressed as:
\[
\text{Amount in first vat} = 6x
\]

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 the second vat after \( x \) minutes can be expressed as:
\[
\text{Amount in second vat} = 10 + 4x
\]

To find when the two vats have an equal amount of liquid, we can set the two expressions equal to each other:
\[
6x = 10 + 4x
\]

This equation represents the point in time when both vats will contain the same amount of liquid.