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The problem can be solved by using the concept of time, distance, and speed relationships. Let’s break it down:

### Given:
- The rowing team covers 60 miles with the current.
- They cover 10 miles against the current.
- The rate of the current is 5 miles per hour.
- Time taken in both directions is the same.

Let \( r \) be the rowing team’s speed in still water (miles per hour).

### Speeds:
- **With the current**: Speed = \( r + 5 \) (since the current helps).
- **Against the current**: Speed = \( r - 5 \) (since the current resists).

### Time Equation:
The time taken to travel a distance \( d \) is given by:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]

Since the time is the same for both trips, we set up the equation:

\[
\frac{60}{r + 5} = \frac{10}{r - 5}
\]

Now, let's solve for \( r \), the speed of the rowing team in still water.

### Step 1: Cross Multiply

\[
60(r - 5) = 10(r + 5)
\]

### Step 2: Expand both sides

\[
60r - 300 = 10r + 50
\]

### Step 3: Move all terms involving \( r \) to one side and constants to the other

\[
60r - 10r = 50 + 300
\]

\[
50r = 350
\]

### Step 4: Solve for \( r \)

\[
r = \frac{350}{50} = 7
\]

### Final Answer:
The rowing team’s speed in still water is **7 miles per hour**.

Would you like further clarification or more details on any of these steps?

Here are some related questions to consider:
1. How would the equation change if the current speed was different?
2. What if the distances were different but the time was still the same?
3. How could this problem be solved graphically instead of algebraically?
4. What would happen if the current was faster than the rowing team’s speed in still water?
5. How can the concept of relative speed be applied to other real-world problems?

**Tip**: When solving word problems, always define your variables clearly and break down the information into smaller pieces.

A rowing team rowed 60 miles while going with the current in the same amount of time as it took to row 10 miles going against the current. The rate of the current was 5 miles per hour. Find the rate of the rowing team in still water.

Learn how to find the rowing team's speed in still water using algebra and speed-time-distance relationships. The problem involves solving rational equations and understanding the effect of current on speed. Suitable for Grades 9-10 students.

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