The speed of a boat in still water is 15 km/h and the speed of the stream is 5 km/h if a person travels 36 km upstream and then returns to the starting point then find the average speed of the total journey

Answer

To solve the problem step by step, we need to calculate the average speed of the total journey of the person traveling upstream and then downstream.

### Step 1: Determine the speeds
- Speed of the boat in still water = 15 km/h
- Speed of the stream = 5 km/h

### Step 2: Calculate the effective speeds
- **Upstream speed** (against the current) = Speed of the boat - Speed of the stream
\[ \text{Upstream speed} = 15 \text{ km/h} - 5 \text{ km/h} = 10 \text{ km/h} \]

- **Downstream speed** (with the current) = Speed of the boat + Speed of the stream
\[ \text{Downstream speed} = 15 \text{ km/h} + 5 \text{ km/h} = 20 \text{ km/h} \]

### Step 3: Calculate the time taken for each part of the journey
- **Distance upstream** = 36 km
- **Distance downstream** = 36 km

- **Time taken to travel upstream**:
\[ \text{Time upstream} = \frac{\text{Distance}}{\text{Speed}} = \frac{36 \text{ km}}{10 \text{ km/h}} = 3.6 \text{ hours} \]

- **Time taken to travel downstream**:
\[ \text{Time downstream} = \frac{\text{Distance}}{\text{Speed}} = \frac{36 \text{ km}}{20 \text{ km/h}} = 1.8 \text{ hours} \]

### Step 4: Calculate total time for the journey
\[ \text{Total time} = \text{Time upstream} + \text{Time downstream} = 3.6 \text{ hours} + 1.8 \text{ hours} = 5.4 \text{ hours} \]

### Step 5: Calculate total distance traveled
\[ \text{Total distance} = \text{Distance upstream} + \text{Distance downstream} = 36 \text{ km} + 36 \text{ km} = 72 \text{ km} \]

### Step 6: Calculate average speed
\[ \text{Average speed} = \frac{\text{Total distance}}{\text{Total time}} = \frac{72 \text{ km}}{5.4 \text{ hours}} = \frac{720}{54} = \frac{40}{3} \text{ km/h} \approx 13.33 \text{ km/h} \]

### Final Answer
The average speed of the total journey is approximately **13.33 km/h**.

---