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This problem involves determining the speed of a boat in still water, using the speeds provided for both upstream and downstream travel.

### Let:
- \( v_b \) = speed of the boat in still water (km/h),
- \( v_c \) = speed of the current (km/h).

### Given:
- Speed upstream = 3 km/h,
- Speed downstream = 9 km/h,
- The distance traveled (upstream and downstream) is the same (18 km), but the speed is different due to the current.

When a boat travels **upstream**, the speed of the current opposes the boat's speed, so:
\[
\text{Speed upstream} = v_b - v_c = 3 \, \text{km/h}
\]

When the boat travels **downstream**, the current aids the boat's speed, so:
\[
\text{Speed downstream} = v_b + v_c = 9 \, \text{km/h}
\]

### Step-by-step solution:
Now, we have two equations:
1. \( v_b - v_c = 3 \)
2. \( v_b + v_c = 9 \)

Add both equations:
\[
(v_b - v_c) + (v_b + v_c) = 3 + 9
\]
\[
2v_b = 12 \implies v_b = 6 \, \text{km/h}
\]

Thus, the speed of the boat in still water is **6 km/h**.

Would you like more details on how these equations were derived?

### Related Questions:
1. How would the problem change if the current's speed were doubled?
2. What would the boat's speed in still water be if the upstream speed was 4 km/h and downstream was 10 km/h?
3. How do the relative speeds change if the boat travels a shorter or longer distance?
4. Can this type of problem be solved graphically using vectors?
5. What would happen if the boat's speed equaled the current's speed?

### Tip:
Always remember, the downstream speed is increased by the current, while the upstream speed is reduced by the current.

A boat while travelling upstream covers a distance of 18 km at the speed of 3 km/hr, whereas while travelling downstream it covers the same distance at a speed of 9 km/hr. What is the speed of the boat in still waters?

Learn how to find the speed of a boat in still water when given upstream and downstream speeds. This example involves solving a linear equation with two variables. Suitable for students in Grades 6-8.

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