wo pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have the same amount of liquid?

Question

wo pumps are filling large vats of liquid. One vat is empty, and the pump is filling it at a rate of 6 gallons per minute. The other vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. When will the two vats have the same amount of liquid?

Answer 1

Let's call the time it takes for the two vats to have the same amount of liquid "t".

At time "t", the first vat will have 6t gallons of liquid.

At time "t", the second vat will have 28 + 4t gallons of liquid.

To find when the two vats have the same amount of liquid, we can set these two expressions equal to each other:

6t = 28 + 4t

Simplifying:

2t = 28

t = 14

Therefore, it will take 14 minutes for the two vats to have the same amount of liquid.

Answer 2

To find out when the two vats will have the same amount of liquid, we need to set up an equation based on the information given.

Let's assume t minutes have passed since the pumps started filling.

The first vat is initially empty and is being filled at a rate of 6 gallons per minute. Therefore, the amount of liquid in the first vat after t minutes will be 6t gallons.

The second vat already contains 28 gallons and is continuing to fill at a rate of 4 gallons per minute. So, the total amount of liquid in the second vat after t minutes will be 28 + 4t gallons.

To find when the two vats have the same amount of liquid, we need to set up an equation:

6t = 28 + 4t

Now, we can solve this equation for t:

6t - 4t = 28
2t = 28
t = 28/2
t = 14

So, the two vats will have the same amount of liquid after 14 minutes.

Answer 3

To find out when the two vats will have the same amount of liquid, we can set up an equation.

Let's assume t represents the time in minutes.

For the empty vat, we know the rate of filling is 6 gallons per minute. So, the amount of liquid in the empty vat after t minutes is 6t.

For the vat with 28 gallons already, we know the rate of filling is 4 gallons per minute. So, the amount of liquid in the vat after t minutes is 28 + 4t.

To find when the two vats have the same amount of liquid, we can set up the equation:

6t = 28 + 4t

Now, we can solve for t:

6t - 4t = 28
2t = 28
t = 28 / 2
t = 14

Therefore, the two vats will have the same amount of liquid after 14 minutes.