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Let's solve the problem step-by-step.

### Problem Analysis:
1. Let \( r \) be the rate of the rowing team in still water (in miles per hour).
2. The rate of the current is 6 miles per hour.

### Scenario 1: Rowing with the current
- Effective speed when rowing with the current: \( r + 6 \) mph.
- Distance rowed: 100 miles.
- Time taken: \( \frac{100}{r + 6} \) hours.

### Scenario 2: Rowing against the current
- Effective speed when rowing against the current: \( r - 6 \) mph.
- Distance rowed: 20 miles.
- Time taken: \( \frac{20}{r - 6} \) hours.

Since the times are equal, we set up the equation:
\[
\frac{100}{r + 6} = \frac{20}{r - 6}
\]

### Solving the Equation:
Let's solve this equation for \( r \). 

1. Cross-multiply:
   \[
   100(r - 6) = 20(r + 6)
   \]
2. Expand:
   \[
   100r - 600 = 20r + 120
   \]
3. Combine like terms:
   \[
   100r - 20r = 120 + 600
   \]
   \[
   80r = 720
   \]
4. Divide by 80:
   \[
   r = 9
   \]

### Answer:
The rate of the rowing team in still water is **9 miles per hour**.

Would you like a detailed explanation of each step, or do you have any questions? 

Here are some related questions you might consider:
1. How would the time change if the current speed was different?
2. What if the distances were different, how would the calculations be adjusted?
3. How can you verify the answer by plugging values back into the original scenario?
4. What happens if the rowing team’s rate equals the current speed?
5. How can this problem be solved using a different method, such as graphing?

**Tip:** When dealing with rate problems, carefully set up the time equations and cross-multiply to find unknown rates effectively.

A rowing team rowed 100 miles while going with the current in the same amount of time as it took to row 20 miles going against the current. The rate of the current was 6 miles per hour. Find the rate of the rowing team in still water.

This problem involves finding the rate of a rowing team in still water given the current speed. Learn how to set up equations and solve for the unknown rate using distance, rate, and time relationships. Suitable for Grades 8-10 students.

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