Question
There are two different cats, the first vat has 12 gallons and is being filled at a rate of 3 gallons per minute. The second vat has 108 gallons and is leaking fluid at 7 gallons per minute. After how many seconds when will both bats have the same amount of liquid?
Answers
GPT 3.5
We can set up an equation to solve this problem. Let's assume $t$ minutes have passed.
The amount of liquid in the first vat after $t$ minutes will be $12 + 3t$ gallons.
The amount of liquid in the second vat after $t$ minutes will be $108 - 7t$ gallons.
To determine when both vats have the same amount of liquid, we set the two expressions equal to each other and solve for $t$:
$12 + 3t = 108 - 7t$
Adding $7t$ to both sides: $12 + 10t = 108$
Subtracting $12$ from both sides: $10t = 96$
Dividing by $10$: $t = 9.6$ minutes.
Since there are 60 seconds in 1 minute, we multiply $9.6$ by $60$ to convert it into seconds.
$9.6 \times 60 = \boxed{576}$ seconds. Answer: \boxed{576}.
The amount of liquid in the first vat after $t$ minutes will be $12 + 3t$ gallons.
The amount of liquid in the second vat after $t$ minutes will be $108 - 7t$ gallons.
To determine when both vats have the same amount of liquid, we set the two expressions equal to each other and solve for $t$:
$12 + 3t = 108 - 7t$
Adding $7t$ to both sides: $12 + 10t = 108$
Subtracting $12$ from both sides: $10t = 96$
Dividing by $10$: $t = 9.6$ minutes.
Since there are 60 seconds in 1 minute, we multiply $9.6$ by $60$ to convert it into seconds.
$9.6 \times 60 = \boxed{576}$ seconds. Answer: \boxed{576}.