There are two different vats. The first vat has 20 gallons is being filled at a rate of 0.5 gallons per minute. The second vat has 128 gallons and is leaking fluid at a rate of 1.5 gallons per minute. After how many seconds will both vats have the same amount of liquid?
____ minutes
To find the number of minutes it takes for both vats to have the same amount of liquid, we can set up an equation. Let's call the number of minutes it takes for this to happen x.
After x minutes, the first vat will have 20 + 0.5x gallons of liquid.
After x minutes, the second vat will have 128 - 1.5x gallons of liquid.
To find the point when they have the same amount of liquid, we'll set these two expressions equal to each other and solve for x:
20 + 0.5x = 128 - 1.5x
First, let's combine the x terms on one side of the equation:
0.5x + 1.5x = 128 - 20
2x = 108
Next, divide both sides of the equation by 2 to solve for x:
x = 54
Therefore, it will take 54 minutes for both vats to have the same amount of liquid.
To convert this to seconds, we multiply by 60 (since there are 60 seconds in a minute):
54 minutes * 60 seconds/minute = 3240 seconds
So, after 3240 seconds, both vats will have the same amount of liquid.