Question

Two pumps are being filled by two different pumps. The first that has 12 gallons is being filled at the rate of 20 gallons per second that the second that has 30 gallons. It is being filled at the rate of 16 gallons per second after how many seconds will both that have the same amount of liquid

Answer 1

Let's denote the amount of liquid in the first tank (which starts with 12 gallons) as \( A(t) \) and the amount in the second tank (which starts with 30 gallons) as \( B(t) \).

The first tank's amount as a function of time \( t \) (in seconds) can be expressed as:

\[
A(t) = 12 + 20t
\]

The second tank's amount can be expressed as:

\[
B(t) = 30 + 16t
\]

We want to find the time \( t \) when both tanks have the same amount of liquid, so we set \( A(t) \) equal to \( B(t) \):

\[
12 + 20t = 30 + 16t
\]

Now, let's solve for \( t \):

1. Subtract \( 16t \) from both sides:
\[
12 + 20t - 16t = 30
\]
\[
12 + 4t = 30
\]

2. Subtract 12 from both sides:
\[
4t = 30 - 12
\]
\[
4t = 18
\]

3. Divide both sides by 4:
\[
t = \frac{18}{4} = 4.5
\]

Therefore, after **4.5 seconds**, both tanks will have the same amount of liquid.