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 is filled 104 cans of soup. It feels cans at a rate of 13 cans per minute right and solve an equation to show when the two machines have the same number of cans of soup.
Let's denote the time (in minutes) it takes for the machines to have the same number of cans of soup by "t".
The number of cans of soup the first machine fills in "t" minutes can be represented by the equation:
16t
The number of cans of soup the second machine fills in "t" minutes can be represented by the equation:
13t
To find when the two machines have the same number of cans of soup, we set the two equations equal to each other and solve for "t":
16t = 13t
Subtracting 13t from both sides:
16t - 13t = 13t - 13t
3t = 0
Dividing both sides by 3:
t = 0
Therefore, the two machines will have the same number of cans of soup after 0 minutes.
Let's assume that t represents the number of minutes it takes for the two machines to have the same number of cans of soup.
For the first machine, the number of cans filled, y1, is given by the equation:
y1 = 16t + 92
For the second machine, the number of cans filled, y2, is given by the equation:
y2 = 13t + 104
To find when the two machines have the same number of cans of soup, we can set y1 equal to y2 and solve the equation.
16t + 92 = 13t + 104
Subtracting 13t from both sides gives:
16t - 13t + 92 = 13t - 13t + 104
3t + 92 = 104
Subtracting 92 from both sides gives:
3t + 92 - 92 = 104 - 92
3t = 12
Dividing both sides by 3 gives:
3t/3 = 12/3
t = 4
Therefore, the two machines will have the same number of cans of soup after 4 minutes.
To find when the two machines have the same number of cans of soup, we can set up an equation. Let's first define the variables:
Let x be the number of minutes for the first machine.
Let y be the number of minutes for the second machine.
The number of cans of soup filled by the first machine is given by:
Number of cans filled by first machine = Rate of filling by first machine × Number of minutes (x)
Number of cans filled by first machine = 16x
Similarly, the number of cans of soup filled by the second machine is:
Number of cans filled by second machine = Rate of filling by second machine × Number of minutes (y)
Number of cans filled by second machine = 13y
Now we can set up the equation to find when they have the same number of cans of soup:
16x = 13y
To solve this equation, we need to find values of x and y that satisfy this condition. One way to do this is to try different values for one variable and find the corresponding value for the other variable until we get a match.
In this case, we can start by plugging in values for x and calculating the corresponding value for y. We know that the first machine has already filled 92 cans, so we can let x = 6 (minutes). Plugging this into the equation:
16(6) = 13y
96 = 13y
Now we need to solve for y by dividing both sides of the equation by 13:
96 / 13 = 13y / 13
7.38 ≈ y
Therefore, when the first machine has been running for 6 minutes, the second machine would have filled approximately 7.38 cans of soup.
To find a more precise time when the two machines have filled the same number of cans, you can continue this process by trying different values for x and solving for y.