2 vats are being filled by 2 diffrent 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

Question

2 vats are being filled by 2 diffrent 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

Answer 1

Let's set up an equation to represent the situation:

Let x be the number of seconds it takes for both vats to have the same amount of liquid.

For the first vat:
Amount in vat = initial amount + rate * time
Amount in first vat = 10 + 12x

For the second vat:
Amount in vat = initial amount + rate * time
Amount in second vat = 25 + 10x

Setting both expressions equal to each other:

10 + 12x = 25 + 10x

Simplifying:

12x - 10x = 25 - 10
2x = 15
x = 7.5

After 7.5 seconds, both vats will have the same amount of liquid.

Answer 2

To find out how many seconds it will take for both vats to have the same amount of liquid, we can set up an equation. Let's denote the number of seconds as "t".

For the first vat:
Amount = Initial amount + Rate * Time
Amount = 10 + 12t

For the second vat:
Amount = Initial amount + Rate * Time
Amount = 25 + 10t

Setting both equations equal to each other:
10 + 12t = 25 + 10t

Simplifying the equation:
12t - 10t = 25 - 10
2t = 15
t = 15/2 = 7.5

So, after 7.5 seconds, both vats will have the same amount of liquid.

Answer 3

To find the number of seconds it takes for both vats to have the same amount of liquid, we need to set up an equation.

Let's denote the number of seconds as "t", the amount of liquid in the first vat as "x", and the amount of liquid in the second vat as "y". We know that the first vat has an initial amount of 10 gallons and is being filled at a rate of 12 gallons per second. Therefore, its amount of liquid can be represented as:

x = 10 + 12t

Similarly, the second vat has an initial amount of 25 gallons and is being filled at a rate of 10 gallons per second. Its amount of liquid can be represented as:

y = 25 + 10t

To find the number of seconds when both vats have the same amount of liquid, we set x equal to y:

10 + 12t = 25 + 10t

Now we can solve this equation to find the value of "t". Subtracting 10t from both sides gives:

2t = 15

Dividing both sides by 2, we get:

t = 7.5

Therefore, after 7.5 seconds, both vats will have the same amount of liquid.