Tyler rows 10 km downstream in 2 hours. On the return trip, it takes him 4 hours to travel 8 km. Determine his average rowing speed and the speed of the current

To solve this problem, let's break it down into two parts: Tyler's rowing speed in still water (denoted by \( r \)) and the speed of the current (denoted by \( c \)).

### Downstream Trip:
- Distance = 10 km
- Time = 2 hours
- The effective speed downstream = \( r + c \), since the current assists Tyler.
  
The speed is given by:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{10}{2} = 5 \, \text{km/h}
\]
Thus, \( r + c = 5 \, \text{km/h} \).

### Upstream Trip:
- Distance = 8 km
- Time = 4 hours
- The effective speed upstream = \( r - c \), since the current opposes Tyler.

The speed is given by:
\[
\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{8}{4} = 2 \, \text{km/h}
\]
Thus, \( r - c = 2 \, \text{km/h} \).

### Solving the system of equations:
We now have two equations:
1. \( r + c = 5 \)
2. \( r - c = 2 \)

To solve for \( r \) and \( c \), add the two equations:
\[
(r + c) + (r - c) = 5 + 2
\]
\[
2r = 7 \quad \Rightarrow \quad r = \frac{7}{2} = 3.5 \, \text{km/h}
\]

Now, substitute \( r = 3.5 \) into one of the original equations (let's use \( r + c = 5 \)):
\[
3.5 + c = 5 \quad \Rightarrow \quad c = 5 - 3.5 = 1.5 \, \text{km/h}
\]

### Conclusion:
- Tyler's average rowing speed in still water is \( 3.5 \, \text{km/h} \).
- The speed of the current is \( 1.5 \, \text{km/h} \).

Would you like more details or have any questions?

### Related Questions:
1. What is Tyler's effective speed upstream and downstream?
2. How much time would it take for Tyler to row 15 km downstream?
3. If the current speed doubled, how would the trip times change?
4. What would be the total time for a round trip of 10 km downstream and back, assuming constant speeds?
5. If Tyler's rowing speed increased to 5 km/h, how would this affect his downstream and upstream times?

**Tip:** When solving problems with multiple unknowns, using a system of equations can help efficiently find the solution.

Tyler rows 10 km downstream in 2 hours. On the return trip, it takes him 4 hours to travel 8 km. Determine his average rowing speed and the speed of the current.

Learn how to calculate Tyler's average rowing speed in still water and the speed of the current using a system of linear equations. This problem involves key concepts like speed, distance, and solving simultaneous equations. Suitable for Grades 8-10.

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