P travels for 6 hours at the rate of 5km/hour and for 3 hours at the rate of 6km/hour. The average speed of the journey in km/hour is

Options

A. `3 (1)/(5)`
B. `5(1)/(3)`
C. `1(2)/(9)`
D. `2(2)/(5)`

Answer

To find the average speed of P's journey, we need to follow these steps:

### Step 1: Calculate the distance traveled during each segment of the journey.

1. **First Segment:**
- Time = 6 hours
- Speed = 5 km/hour
- Distance = Speed × Time = 5 km/hour × 6 hours = 30 km

2. **Second Segment:**
- Time = 3 hours
- Speed = 6 km/hour
- Distance = Speed × Time = 6 km/hour × 3 hours = 18 km

### Step 2: Calculate the total distance traveled.

- Total Distance = Distance from First Segment + Distance from Second Segment
- Total Distance = 30 km + 18 km = 48 km

### Step 3: Calculate the total time taken for the journey.

- Total Time = Time for First Segment + Time for Second Segment
- Total Time = 6 hours + 3 hours = 9 hours

### Step 4: Calculate the average speed.

- Average Speed = Total Distance / Total Time
- Average Speed = 48 km / 9 hours = 5.33 km/hour (or 5 1/3 km/hour)

### Final Answer:
The average speed of the journey is **5 1/3 km/hour**.

---