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 vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have the same amount of liquid?(1 point)
They will have the same amount of liquid after
minutes.
Remaining Attempts : 3

Answer 1

To determine when the two vats will have the same amount of liquid, we can set up equations based on the information given.

Let:

• \( t \) be the time in minutes.
• The first vat starts empty and fills at a rate of 6 gallons per minute. Thus, the amount of liquid in the first vat after \( t \) minutes is: \[ A = 6t \]
• The second vat starts with 28 gallons and fills at a rate of 4 gallons per minute. Therefore, the amount of liquid in the second vat after \( t \) minutes is: \[ B = 28 + 4t \]

To find out when both vats have the same amount of liquid, we set \( A \) equal to \( B \): \[ 6t = 28 + 4t \]

Now, let's solve for \( t \):

1. Subtract \( 4t \) from both sides: \[ 6t - 4t = 28 \] \[ 2t = 28 \]

2. Divide by 2: \[ t = 14 \]

Thus, the two vats will have the same amount of liquid after 14 minutes.