When a crew rows with the current, travels 14 in 2 hours Against the currentthe crew rows 2 miles in 2 hoursLet x the crew's rowing rate in still water and let y the rate of the current Find the rate of rowing in still water and the rate of the current

Let \( x \) represent the rowing rate of the crew in still water (miles per hour), and \( y \) represent the rate of the current (miles per hour). We can form two equations based on the information provided:

### 1. **With the current:**
- The effective speed of the crew when rowing with the current is the sum of their still water speed and the current's speed, which is \( x + y \).
- They travel 14 miles in 2 hours, so the speed equation is:
\[
x + y = \frac{14}{2} = 7
\]
### 2. **Against the current:**
- The effective speed of the crew when rowing against the current is their still water speed minus the current's speed, which is \( x - y \).
- They travel 2 miles in 2 hours, so the speed equation is:
\[
x - y = \frac{2}{2} = 1
\]

Now, we have the system of equations:
\[
x + y = 7 \tag{1}
\]
\[
x - y = 1 \tag{2}
\]

### Solving the system:
1. Add equations (1) and (2):
\[
(x + y) + (x - y) = 7 + 1
\]
\[
2x = 8
\]
\[
x = 4
\]

2. Substitute \( x = 4 \) into equation (1):
\[
4 + y = 7
\]
\[
y = 3
\]

### Conclusion:
- The crew's rowing rate in still water is **4 miles per hour**.
- The rate of the current is **3 miles per hour**.

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How would the rowing rates change if the current increased by 1 mile per hour?
2. What is the total distance traveled by the crew with the current over 5 hours?
3. How long would it take the crew to row 10 miles against the current?
4. What if the crew rows in still water? How long will it take them to cover 8 miles?
5. How does changing the current speed affect the rowing time for a fixed distance?

**Tip:** When solving a system of equations, adding or subtracting them directly can often simplify the process.

When a crew rows with the current, travels 14 in 2 hours. Against the current, the crew rows 2 miles in 2 hours. Let x be the crew's rowing rate in still water and let y be the rate of the current. Find the rate of rowing in still water and the rate of the current.

Learn how to solve a system of equations to find the rowing rate in still water and the current speed. The problem involves algebraic concepts such as linear equations and the addition method for solving systems. Suitable for students in Grades 8-10.

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