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.
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.
Let x be the number of minutes it takes for the two machines to have filled the same number of cans of soup.
The equation that represents the situation can be written as:
180 + 15x = 210 + 12x
To find out when the two machines will have filled the same number of cans of soup, we can set up an equation based on the given information.
Let's assume that after t minutes, the first machine will have filled the same number of cans of soup as the second machine.
The number of cans filled by the first machine can be represented by the equation:
Cans filled by machine 1 = 180 + 15t
Similarly, the number of cans filled by the second machine can be represented by the equation:
Cans filled by machine 2 = 210 + 12t
To find the time at which the two machines will have filled the same number of cans, we can set these two equations equal to each other:
180 + 15t = 210 + 12t
Now, we can solve this equation to find the value of t.