Two vats 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?

Question

Two vats 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?

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Answer 1

Let's assume that after "x" seconds, both vats will have the same amount of liquid.

For the first vat:
Initial amount = 10 gallons
Rate of filling = 12 gallons per second

So, the equation for the amount of liquid in the first vat after "x" seconds is:
Amount = 10 + 12x

For the second vat:
Initial amount = 25 gallons
Rate of filling = 10 gallons per second

So, the equation for the amount of liquid in the second vat after "x" seconds is:
Amount = 25 + 10x

Setting these two equations equal to each other:
10 + 12x = 25 + 10x

Simplifying:
12x - 10x = 25 - 10
2x = 15
x = 15/2
x = 7.5 seconds

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

Answer 2

To find the number of seconds when both vats have the same amount of liquid, we can set up an equation based on the rates at which the vats are being filled.

Let's denote the number of seconds it takes for both vats to have the same amount of liquid as "t". At time "t", the first vat will have 10 + 12t gallons, and the second vat will have 25 + 10t gallons.

We can set up the following equation to represent the situation:
10 + 12t = 25 + 10t

To solve for "t", we will isolate the variable:
12t - 10t = 25 - 10
2t = 15
t = 15/2
t = 7.5

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

Answer 3

To find out when both vats will have the same amount of liquid, we can set up an equation based on their rates of filling.

Let's assume that after "t" seconds, both vats will have the same amount of liquid.

For the first vat, the amount of liquid will be 10 gallons + (12 gallons/second) * t seconds.
For the second vat, the amount of liquid will be 25 gallons + (10 gallons/second) * t seconds.

Now we can set up an equation to find when the two amounts are equal:

10 + 12t = 25 + 10t

Simplifying the equation:

12t - 10t = 25 - 10

2t = 15

t = 15/2

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