Question

Two machines at a factory are filling cans of soup. One machine has filled 92 cans of soup. It fills cans at a rate of 16 cans per minute. The second machine has filled 104 cans of soup. It fills cans at a rate of 13 cans per minute. Write an equation to show when the two machines will have filled the same number of cans of soup.

Answer 1

Let's assume that after t minutes, the first machine will have filled x cans of soup, and the second machine will have filled y cans of soup.

For the first machine, we can use the formula:

x = 16t + 92

For the second machine, we can use the formula:

y = 13t + 104

To find when the two machines will have filled the same number of cans of soup, we need to solve for t when x = y:

16t + 92 = 13t + 104

Simplifying the equation:

3t = 12

t = 4

Therefore, the two machines will have filled the same number of cans of soup after 4 minutes.