When a crew rows with the current, travels 10 in 2 hoursAgainst the currentthe crew rows 6 miles in 2 hoursLet x the crew's rowing rate in water and let the rate of the current Find the rate of rowing in water and the rate of the current

Let the crew's rowing rate in still water be \( x \) (in miles per hour), and the rate of the current be \( y \) (in miles per hour).

### Step 1: Define the problem using equations.
1. When rowing **with the current**, the effective speed of the crew is \( x + y \). The distance traveled is 10 miles in 2 hours. Therefore, we can set up the following equation for this case:
   \[
   x + y = \frac{10}{2} = 5 \quad \text{(miles per hour)}
   \]

2. When rowing **against the current**, the effective speed of the crew is \( x - y \). The distance traveled is 6 miles in 2 hours. Therefore, we can set up the following equation for this case:
   \[
   x - y = \frac{6}{2} = 3 \quad \text{(miles per hour)}
   \]

### Step 2: Solve the system of equations.
Now, we have the following system of equations:
\[
x + y = 5
\]
\[
x - y = 3
\]

Add the two equations together to eliminate \( y \):
\[
(x + y) + (x - y) = 5 + 3
\]
\[
2x = 8
\]
\[
x = 4
\]

Now, substitute \( x = 4 \) into the first equation:
\[
4 + y = 5
\]
\[
y = 1
\]

### Step 3: Conclusion.
- The rowing rate of the crew in still water is \( \mathbf{4} \) miles per hour.
- The rate of the current is \( \mathbf{1} \) mile per hour.

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Would you like more details or have any questions?

Here are 5 related questions:
1. How would the rowing time change if the current increased by 1 mile per hour?
2. What happens if the current slows down to 0.5 miles per hour?
3. How would you adjust the equation if the distance against the current were different?
4. Can you derive a formula for the general case of rowing with and against the current?
5. How would wind affect the effective rowing rate?

**Tip:** When solving a system of equations, adding or subtracting the equations can simplify the solution by eliminating one variable.

When a crew rows with the current, travels 10 in 2 hours. Against the current, the crew rows 6 miles in 2 hours. Let x be the crew's rowing rate in water and let the rate of the current be y. Find the rate of rowing in water and the rate of the current.

Learn how to solve a real-world algebra problem involving rowing with and against a current. This problem involves solving a system of linear equations to find the rowing rate and the speed of the current. Suitable for students in Grades 8-10.

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