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?
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}.
To find out when both vats will have the same amount of liquid, we need to set up an equation using the rate of filling and the rate of leaking.
Let's assume that after t minutes, both vats will have the same amount of liquid.
For the first vat, the amount of liquid in it after t minutes can be calculated as:
Amount of liquid = Initial amount + (Rate of filling * t)
Amount of liquid in the first vat = 12 + (3 * t) gallons
For the second vat, the amount of liquid in it after t minutes can be calculated as:
Amount of liquid = Initial amount - (Rate of leaking * t)
Amount of liquid in the second vat = 108 - (7 * t) gallons
Setting the two equations equal to each other:
12 + (3 * t) = 108 - (7 * t)
Simplifying the equation:
3 * t + 7 * t = 108 - 12
10 * t = 96
t = 9.6
Therefore, it will take 9.6 minutes or 9.6 * 60 = 576 seconds for both vats to have the same amount of liquid.
To find out the time when both vats will have the same amount of liquid, we can set up an equation. Let's assume the time in minutes as 't'.
For the first vat, the amount of liquid in it can be represented by the equation:
12 + 3t (where 3t represents the amount of liquid being filled per minute).
For the second vat, the amount of liquid in it can be represented by the equation:
108 - 7t (where 7t represents the amount of liquid being leaked per minute).
Now, we can set these two equations equal to each other to find out when both vats will have the same amount of liquid:
12 + 3t = 108 - 7t
To solve for 't', let's simplify the equation:
10t = 96
Dividing both sides by 10, we get:
t = 9.6 minutes
Since we're looking for the time in seconds, we can multiply 9.6 minutes by 60 (since 1 minute has 60 seconds):
t = 576 seconds
Therefore, both vats will have the same amount of liquid after 576 seconds.