A boat goes 20 km downstream in one hour and the same distance upstream in two hours. What is the speed of the boat in still water?

Answer

To solve the problem step by step, we will use the information given about the boat's downstream and upstream travel.

### Step 1: Define Variables
Let:
- \( x \) = speed of the boat in still water (in km/h)
- \( y \) = speed of the stream (in km/h)

### Step 2: Write Down the Speed Equations
The speed of the boat downstream (with the current) is:
\[ \text{Speed downstream} = x + y \]

The speed of the boat upstream (against the current) is:
\[ \text{Speed upstream} = x - y \]

### Step 3: Use the Downstream Information
The boat travels 20 km downstream in 1 hour. Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
We can write:
\[ 1 = \frac{20}{x + y} \]
From this, we can rearrange to find:
\[ x + y = 20 \quad \text{(Equation 1)} \]

### Step 4: Use the Upstream Information
The boat travels the same distance (20 km) upstream in 2 hours. Again using the time formula:
\[ 2 = \frac{20}{x - y} \]
Rearranging gives us:
\[ x - y = 10 \quad \text{(Equation 2)} \]

### Step 5: Solve the System of Equations
Now we have a system of two equations:
1. \( x + y = 20 \) (Equation 1)
2. \( x - y = 10 \) (Equation 2)

We can add these two equations together:
\[ (x + y) + (x - y) = 20 + 10 \]
This simplifies to:
\[ 2x = 30 \]
Dividing both sides by 2 gives:
\[ x = 15 \]

### Step 6: Find the Speed of the Stream
Now, we can substitute \( x \) back into one of the equations to find \( y \). Using Equation 1:
\[ 15 + y = 20 \]
Subtracting 15 from both sides gives:
\[ y = 5 \]

### Conclusion
The speed of the boat in still water is \( \boxed{15} \) km/h.

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