Two pumps are large vats of liquidOne vat is emptyand the pump is it at a rate of 6 gallons per minuteThe other is already filled with 10 gallons , and it is continuing to fill at a rate of 4 gallons per minute Write an equation to show when the will have an equal amount of liquid Use as your variable point )
Let t be the time in minutes.
Let V1(t) be the amount of liquid in the first vat at time t.
Let V2(t) be the amount of liquid in the second vat at time t.
Since one vat is empty and the pump is filling it at a rate of 6 gallons per minute, the equation for V1(t) is:
V1(t) = 6t
Since the other vat is already filled with 10 gallons and is continuing to fill at a rate of 4 gallons per minute, the equation for V2(t) is:
V2(t) = 10 + 4t
To find when the two vats will have an equal amount of liquid, we need to solve the equation:
V1(t) = V2(t)
6t = 10 + 4t
Solving for t:
6t - 4t = 10
2t = 10
t = 5
Therefore, the two vats will have an equal amount of liquid after 5 minutes.