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.