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 a rate of 4 gallons per minute. Write an equation to show when the two vats will have an equal amount of liquid. Use x

Question

as your variable. (2 points)
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Answer 1

To compare the amounts of liquid in the two vats over time, we can set up an equation based on the information provided.

Let's define \( x \) as the time in minutes.

1. For the first vat (which starts empty and fills at 6 gallons per minute): \[ \text{Amount in first vat} = 6x \]

2. For the second vat (which starts with 10 gallons and fills at 4 gallons per minute): \[ \text{Amount in second vat} = 10 + 4x \]

Now, to find out when both vats have an equal amount of liquid, we set these two expressions equal to each other:

\[ 6x = 10 + 4x \]

Thus, the equation to represent the situation is:

\[ 6x = 10 + 4x \]

Answer 2

GPT-4o mini Wrong