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 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?

Answer 1

Let's assume that after t minutes, the two vats will have the same amount of liquid.

Let V be the amount of liquid in the first vat after t minutes, and let W be the amount of liquid in the second vat after t minutes.

The amount of liquid in the first vat after t minutes is given by:

V = 6t

The amount of liquid in the second vat after t minutes is given by:

W = 28 + 4t

To find when the two vats have the same amount of liquid, we need to solve the equation:

V = W

6t = 28 + 4t

2t = 28

t = 14

Therefore, the two vats will have the same amount of liquid after 14 minutes.