Two vats are being filled by two different pumps. The first vat has 10 gallons is being filled at a rate of 12 gallons per second. The second vat has 25 gallons and is being filled at a rate of 10 gallons per second. After how many seconds will both vats have the same amount of liquid?

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1 answer

Let's assume that after "x" seconds, both vats will have the same amount of liquid.

For the first vat:
Initial amount = 10 gallons
Rate of filling = 12 gallons per second

So, the equation for the amount of liquid in the first vat after "x" seconds is:
Amount = 10 + 12x

For the second vat:
Initial amount = 25 gallons
Rate of filling = 10 gallons per second

So, the equation for the amount of liquid in the second vat after "x" seconds is:
Amount = 25 + 10x

Setting these two equations equal to each other:
10 + 12x = 25 + 10x

Simplifying:
12x - 10x = 25 - 10
2x = 15
x = 15/2
x = 7.5 seconds

After 7.5 seconds, both vats will have the same amount of liquid.