Two pumps are being filled by two different pumps. The first vat has 10 gallons is being filled at a rate of 12 gallons per second. The second vat has 25 gallons and is being filled at a rate of 10 gallons per second. After how many seconds will both vats have the same amount of liquid?
Let $t$ be the number of seconds it takes for the vats to have the same amount of liquid. In $t$ seconds, the first vat will have $10+12t$ gallons and the second vat will have $25+10t$ gallons. Setting these two expressions equal to each other creates the equation $10+12t=25+10t$. Subtracting 10 from both sides gives $12t-10t=25-10$, which simplifies to $2t=15$. Dividing both sides by 2 gives $t=\boxed{7.5}$ seconds.
answer?
To find out when both vats will have the same amount of liquid, we can set up an equation based on the given information.
Let's assume that after "t" seconds, both vats will have the same amount of liquid.
For the first vat:
Amount of liquid = Initial amount + (filling rate × time)
Amount of liquid in the first vat = 10 + (12t)
For the second vat:
Amount of liquid = Initial amount + (filling rate × time)
Amount of liquid in the second vat = 25 + (10t)
When both vats have the same amount of liquid, the equations will be equal:
10 + 12t = 25 + 10t
To solve this equation for "t," we can subtract 10t from both sides:
12t - 10t = 25 - 10
Simplifying:
2t = 15
Now, divide both sides of the equation by 2 to isolate "t":
(2t) / 2 = 15 / 2
t = 15 / 2
Therefore, after approximately 7.5 seconds, both vats will have the same amount of liquid.
To find out when both vats will have the same amount of liquid, we can set up an equation and solve for the time it takes.
Let's assume the number of seconds needed is "t". At time "t", the first vat will have 10 + 12t gallons, and the second vat will have 25 + 10t gallons.
We want to find the value of "t" when both vats have the same amount of liquid. So we can set up the equation:
10 + 12t = 25 + 10t
To solve for "t", we can start by subtracting 10t from both sides of the equation:
12t - 10t = 25 - 10
This simplifies to:
2t = 15
Finally, divide both sides of the equation by 2:
t = 15 / 2
Therefore, both vats will have the same amount of liquid after 7.5 seconds.