To solve this problem, we need to set up an equation where the number of cans filled by the first machine is equal to the number of cans filled by the second machine.
Let x be the number of minutes it takes for the two machines to have filled the same number of cans.
For the first machine: number of cans filled = 92 + 16x
For the second machine: number of cans filled = 104 + 13x
Setting these two expressions equal to each other, we get:
92 + 16x = 104 + 13x
Now, we can solve this equation to find the value of x.
Subtract 13x from both sides:
92 + 3x = 104
Subtract 92 from both sides:
3x = 12
Divide both sides by 3:
x = 4
Therefore, the two machines will have filled the same number of cans of soup after 4 minutes.