John is wrapping tamales. He has already wrapped 6 tamales when his friend Cole arrives to help. John wraps 2 tamales every minute, and Cole wraps 3 tamales every minute.

At this pace, how many minutes will it take for Cole to have wrapped the same number of tamales as John?

Simplify any fractions.

Let's define the variables and analyze the problem step by step.

- John has already wrapped 6 tamales when Cole arrives.
- John wraps 2 tamales per minute.
- Cole wraps 3 tamales per minute.

We need to determine how long it will take for Cole to wrap the same number of tamales as John.

### Step 1: Equation setup
Let \( t \) be the number of minutes after Cole starts wrapping tamales.

- In \( t \) minutes, John wraps \( 2t \) additional tamales. Since he already has 6 wrapped, the total number of tamales John wraps after \( t \) minutes is:
  \[
  \text{John's total tamales} = 6 + 2t
  \]

- In \( t \) minutes, Cole wraps \( 3t \) tamales.

### Step 2: Set up the equation
We want to find the time when the number of tamales Cole has wrapped equals the number of tamales John has wrapped. Therefore, we set their totals equal to each other:
\[
6 + 2t = 3t
\]

### Step 3: Solve for \( t \)
Now, solve the equation:
\[
6 + 2t = 3t
\]
Subtract \( 2t \) from both sides:
\[
6 = t
\]

### Step 4: Conclusion
It will take Cole **6 minutes** to wrap the same number of tamales as John.

Would you like a detailed explanation of any part of this solution?

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Here are 5 related questions to explore:

1. How many total tamales will both John and Cole have wrapped after 6 minutes?
2. If Cole wrapped 4 tamales per minute instead of 3, how long would it take him to catch up to John?
3. How many tamales does John wrap in 10 minutes without Cole's help?
4. If both John and Cole continue wrapping, how many tamales will they wrap together in 15 minutes?
5. What if John slowed down to 1 tamale per minute after 6 minutes? How long would it take Cole to catch up?

**Tip:** When setting up equations, identify the rate of change (like tamales per minute) for each person or object involved to ensure correct comparison over time.

John is wrapping tamales. He has already wrapped 6 tamales when his friend Cole arrives to help. John wraps 2 tamales every minute, and Cole wraps 3 tamales every minute. At this pace, how many minutes will it take for Cole to have wrapped the same number of tamales as John?

Solve this linear equation problem: John wraps tamales at 2 per minute, and Cole wraps 3 per minute. Find out how many minutes it takes for Cole to catch up to John's total of wrapped tamales, starting with John already having 6 wrapped. Suitable for Grades 6-8.

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