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

Question

as your variable. (2 points)
[
]×=[
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dont forget to use the multiplication sign

Answer 1

Let \( x \) represent the number of minutes that have passed.

For the first vat, which starts empty and is filling at a rate of 6 gallons per minute, the amount of liquid in the vat after \( x \) minutes can be represented as:

\[ 6 \times x \]

For the second vat, which starts with 10 gallons and fills at a rate of 4 gallons per minute, the amount of liquid in that vat after \( x \) minutes can be represented as:

\[ 10 + 4 \times x \]

To find the point at which both vats have the same amount of liquid, we can set these two expressions equal to each other:

\[ 6 \times x = 10 + 4 \times x \]

This equation shows when the two vats will have an equal amount of liquid.