Let's assume that after x minutes, the amount of liquid in the empty vat is y gallons.
Since the empty vat is being filled at a rate of 6 gallons per minute, the equation for the amount of liquid in the empty vat after x minutes is y = 6x.
The other vat is already filled with 10 gallons and is continuing to fill at a rate of 4 gallons per minute. So, the equation for the amount of liquid in the other vat after x minutes is y = 10 + 4x.
We want to find when the two vats will have an equal amount of liquid, so we can set the two equations equal to each other:
6x = 10 + 4x.
Simplifying the equation, we have:
6x - 4x = 10.
2x = 10.
Dividing both sides by 2, we get:
x = 5.
Therefore, after 5 minutes, the two vats will have an equal amount of liquid.
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 is already filled with 10 gallons, and it is continuing to fill at rate of 4 gallons per minute. Write an equation to show when the two vats will have an equal amount of liquid. Use x as your variable
1 answer
1 answer