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.
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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