A boat can travel at a speed of 6 km/h upstream and 15 km/h downstream. If it distance of 30 km upstream and 60 km downstream, then the average speed for the entire journey is _______

Answer

To find the average speed for the entire journey of the boat, we need to follow these steps:

### Step 1: Calculate the time taken to travel upstream
The speed of the boat upstream is 6 km/h, and the distance traveled upstream is 30 km.

Using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
We can calculate the time taken to travel upstream:
\[ \text{Time}_{\text{upstream}} = \frac{30 \text{ km}}{6 \text{ km/h}} = 5 \text{ hours} \]

### Step 2: Calculate the time taken to travel downstream
The speed of the boat downstream is 15 km/h, and the distance traveled downstream is 60 km.

Using the same formula:
\[ \text{Time}_{\text{downstream}} = \frac{60 \text{ km}}{15 \text{ km/h}} = 4 \text{ hours} \]

### Step 3: Calculate the total time for the journey
Now, we need to add the time taken for both upstream and downstream journeys:
\[ \text{Total Time} = \text{Time}_{\text{upstream}} + \text{Time}_{\text{downstream}} = 5 \text{ hours} + 4 \text{ hours} = 9 \text{ hours} \]

### Step 4: Calculate the total distance traveled
The total distance traveled is the sum of the distances traveled upstream and downstream:
\[ \text{Total Distance} = 30 \text{ km} + 60 \text{ km} = 90 \text{ km} \]

### Step 5: Calculate the average speed
Finally, we can calculate the average speed using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]
Substituting the values we found:
\[ \text{Average Speed} = \frac{90 \text{ km}}{9 \text{ hours}} = 10 \text{ km/h} \]

### Final Answer
The average speed for the entire journey is **10 km/h**.

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