To find out when the two machines will have filled the same number of cans of soup, we can set up equations to represent the total number of cans filled by each machine over time.
Let \( t \) be the number of minutes after the current time.
Machine 1:
- It has already filled 92 cans.
- It fills at a rate of 16 cans per minute.
- The total number of cans filled by Machine 1 after \( t \) minutes is: \[ 92 + 16t \]
Machine 2:
- It has already filled 104 cans.
- It fills at a rate of 13 cans per minute.
- The total number of cans filled by Machine 2 after \( t \) minutes is: \[ 104 + 13t \]
Now, we need to find the time \( t \) when both machines will have filled the same number of cans, which gives us the equation: \[ 92 + 16t = 104 + 13t \]
Next, we can solve this equation:
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Subtract \( 13t \) from both sides: \[ 92 + 3t = 104 \]
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Subtract 92 from both sides: \[ 3t = 12 \]
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Divide both sides by 3: \[ t = 4 \]
So, the two machines will have filled the same number of cans in \( 4 \) minutes.
Total cans filled by each machine after 4 minutes:
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For Machine 1: \[ 92 + 16 \cdot 4 = 92 + 64 = 156 \]
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For Machine 2: \[ 104 + 13 \cdot 4 = 104 + 52 = 156 \]
Both machines will have filled 156 cans after 4 minutes.