Two pumps 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?
2 answers
Let $t$ be the number of seconds it takes for the vats to have the same amount of liquid. In $t$ seconds, the first vat will have $10+12t$ gallons and the second vat will have $25+10t$ gallons. Setting these two expressions equal to each other creates the equation $10+12t=25+10t$. Subtracting 10 from both sides gives $12t-10t=25-10$, which simplifies to $2t=15$. Dividing both sides by 2 gives $t=\boxed{7.5}$ seconds.
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