A man completes 30 km of a journey at 6 km/h and the remaining 40 km of the journey in 5 h. Find the average speed for the whole journery.

Options

A. `6(4)/(11)`km/h
B. `7`km/h
C. `7 (1)/(2) `km/h
D. `8` km/h

Answer

To find the average speed for the whole journey, we will follow these steps:

### Step 1: Calculate the total distance of the journey.
The man travels two segments of the journey:
- First segment: 30 km
- Second segment: 40 km

**Total Distance = 30 km + 40 km = 70 km**

### Step 2: Calculate the time taken for each segment of the journey.
1. **Time for the first segment (T1)**:
- Distance = 30 km
- Speed = 6 km/h
- Time = Distance / Speed = 30 km / 6 km/h = 5 hours

2. **Time for the second segment (T2)**:
- The time for this segment is given as 5 hours.

### Step 3: Calculate the total time taken for the journey.
**Total Time = T1 + T2 = 5 hours + 5 hours = 10 hours**

### Step 4: Calculate the average speed for the whole journey.
The formula for average speed is:
**Average Speed = Total Distance / Total Time**

Substituting the values we found:
**Average Speed = 70 km / 10 hours = 7 km/h**

### Final Answer:
The average speed for the whole journey is **7 km/h**.

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