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 vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have
the same amount of liquid? (1 point)
Let t be the time (in minutes) it takes for the two vats to have the same amount of liquid.
After t minutes, the vat that was initially empty will have been filled with 6t gallons.
The vat that initially contained 28 gallons will have been filled with 4t + 28 gallons.
Setting these two expressions equal to each other, we have:
6t = 4t + 28
2t = 28
t = 14
Therefore, the two vats will have the same amount of liquid after 14 minutes. Answer: \boxed{14}.
To find out when the two vats will have the same amount of liquid, we can set up an equation based on the rates at which they are filling.
Let's assume the time (in minutes) it takes for the two vats to have the same amount of liquid is represented by t.
For the first vat (empty vat), the amount of liquid after t minutes is 6t (since it is being filled at a rate of 6 gallons per minute).
For the second vat (already containing 28 gallons), the amount of liquid after t minutes is 28 + 4t (since it is being filled at a rate of 4 gallons per minute and already contains 28 gallons).
We set up an equation to find when the two vats have the same amount of liquid:
6t = 28 + 4t
Simplifying the equation:
6t - 4t = 28
2t = 28
t = 14
Therefore, it will take 14 minutes for the two vats to have the same amount of liquid.