Linear Equations in Real-World Scenarios Practice

Question

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Question
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
as your variable. (2 points)
[
]×=[
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]
Remaining Attempts : 1

Answer 1

To find out when the two vats will have the same amount of liquid, let's set up equations for each vat based on the information provided.

1. For the first vat, which starts empty and fills at a rate of 6 gallons per minute, we can express the amount of liquid in terms of \( x \) (the number of minutes) as: \[ \text{Amount in vat 1} = 6x \]

2. For the second vat, which starts with 10 gallons and fills at a rate of 4 gallons per minute, the amount of liquid in this vat can be represented as: \[ \text{Amount in vat 2} = 10 + 4x \]

Now, we want to find when these two amounts are equal, so we set up the equation: \[ 6x = 10 + 4x \]

This is the equation you need to solve to find the value of \( x \) when both vats have the same amount of liquid.