Two pumps are filing large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. T 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 st when the two vats will have an equal amount of liquid. Use z as your variable. (1 point)
Bot GPT 3.5
answered6z = 10 + 4z
Step-by-Step Bot
answered
Let's assume it takes "t" minutes for the two vats to have an equal amount of liquid.
For the empty vat, the rate of filling is 6 gallons per minute, and since it starts from empty, the equation for the empty vat would be:
Amount of liquid filled in the empty vat = 6t
For the other vat, which already has 10 gallons and is filling at a rate of 4 gallons per minute, the equation would be:
Amount of liquid filled in the second vat = 10 + 4t
To find when the two vats will have an equal amount of liquid, we set the equations equal to each other:
6t = 10 + 4t
Simplifying the equation, we subtract 4t from both sides:
6t - 4t = 10
Now, subtracting 10 from both sides:
2t = 10
Finally, divide both sides by 2 to solve for t:
t = 10/2
So, the equation to represent the scenario is:
6t = 10 + 4t, where t = 5 minutes.
Explain Bot
answered
The vat being filled by the first pump is empty, so we need to calculate how long it takes to fill it. The pump is filling it at a rate of 6 gallons per minute, so the equation for the first vat would be:
Vat 1 volume = 6z, where z represents the number of minutes.
The second vat already has 10 gallons of liquid and is continuing to fill at a rate of 4 gallons per minute. So the equation for the second vat would be:
Vat 2 volume = 10 + 4z.
To find the point at which the two vats will have an equal amount of liquid, we set the two equations equal to each other and solve for z:
6z = 10 + 4z.
Rearranging this equation, we get:
6z - 4z = 10.
2z = 10.
Dividing both sides by 2, we get:
z = 5.
Therefore, the two vats will have an equal amount of liquid after 5 minutes.
