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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Use one multiplication sign one addition sign and one equal sign

Answer 1

To represent the amounts of liquid in each vat as a function of time (in minutes), we can define:

• The amount of liquid in the first vat (which is filling from empty at 6 gallons per minute) after \( x \) minutes is given by the equation: \[ 6x \]

• The amount of liquid in the second vat (which starts with 10 gallons and is filling at 4 gallons per minute) after \( x \) minutes is given by the equation: \[ 10 + 4x \]

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

\[ 6x = 10 + 4x \]

Thus, the final equation showing when the two vats will have an equal amount of liquid is:

\[ 6x = 10 + 4x \]