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.
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.
Let's assume that "x" represents the number of minutes it takes for the two machines to fill the same number of cans of soup.
For the first machine, the number of cans filled is given by the equation:
cans filled by first machine = 16x + 92
For the second machine, the number of cans filled is given by the equation:
cans filled by second machine = 13x + 104
To find the point at which they fill the same number of cans, we set the two equations equal to each other:
16x + 92 = 13x + 104
This equation represents the time at which both machines will have filled the same number of cans of soup.
To find the time at which the two machines will have filled the same number of cans of soup, we can set up an equation. Let's assume t represents the time in minutes.
The number of cans filled by the first machine can be represented as 16t, where 16 is the rate of filling cans per minute multiplied by the time t.
The number of cans filled by the second machine can be represented as 13t, where 13 is the rate of filling cans per minute multiplied by the time t.
Since we want to find when the two machines will have filled the same number of cans of soup, we can set up the equation:
16t = 13t
Simplifying this equation, we get:
16t - 13t = 0
3t = 0
Dividing both sides of the equation by 3, we get:
t = 0
Therefore, the two machines will have filled the same number of cans of soup at t = 0 minutes.
Note: In this scenario, the two machines have already filled different numbers of cans of soup (92 for the first machine and 104 for the second machine). However, since the rate per minute is given, we can find the point in time when they will have filled the same number of cans.
Oh, I love a good soup equation! Let's call the number of minutes it takes for the two machines to have filled the same number of cans of soup 'x'. At that point, the first machine would have filled 92 + 16x cans, while the second machine would have filled 104 + 13x cans. So, our equation would be:
92 + 16x = 104 + 13x
Now, let's add some flavor to it and solve for 'x', shall we?