Question

two machines that effect or filling cans of soup. One machine has filled 92 cans of soup fill cans at a rate of 16 cans per minute. The second machine has filled 104 cans of soap fills cans at a rate of 13 cans per minute right in solve an equation to show when the two machines will filled the same number of cans of soup

Answer 1

To find out when the two machines will have filled the same number of cans of soup, we can set up equations based on the information provided.

Let \( t \) represent the number of minutes after the current point in time.

**Machine 1:**
- Initially filled: 92 cans
- Rate: 16 cans per minute
- Number of cans filled after \( t \) minutes: \( 92 + 16t \)

**Machine 2:**
- Initially filled: 104 cans
- Rate: 13 cans per minute
- Number of cans filled after \( t \) minutes: \( 104 + 13t \)

We want to find \( t \) such that the number of cans filled by both machines is the same:

\[
92 + 16t = 104 + 13t
\]

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

1. Subtract \( 13t \) from both sides:

\[
92 + 16t - 13t = 104
\]

Which simplifies to:

\[
92 + 3t = 104
\]

2. Subtract 92 from both sides:

\[
3t = 104 - 92
\]

This simplifies to:

\[
3t = 12
\]

3. Divide both sides by 3:

\[
t = \frac{12}{3} = 4
\]

Now that we have \( t = 4 \), it means that in 4 minutes, both machines will have filled the same number of cans.

To find out how many cans they will have filled at that time, we can substitute \( t = 4 \) back into either of the equations:

Using Machine 1:

\[
92 + 16(4) = 92 + 64 = 156
\]

Using Machine 2:

\[
104 + 13(4) = 104 + 52 = 156
\]

Thus, after 4 minutes, both machines will have filled **156 cans of soup**.