Question

Two machines at a factory are filling cans of soup. One machine has already filled 180 cans of soup, and fills cans at a rate of 15 per minute. The second machine has already filled 210 cans of soup, and fills cans at a rate of 12 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 = 15t + 180

For the second machine, we can use the formula:

y = 12t + 210

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.

So, we can set the two equations equal to each other:

15t + 180 = 12t + 210

Simplifying the equation:

3t = 30

t = 10

Therefore, the two machines will have filled the same number of cans of soup after 10 minutes.