A man travels 600 Km by train at 80 Km/hour, 600 Km by ship at 30 Km/hour, 500 Km by aeroplane at 400 Km/hour and 300 Km by car at 60 Km/hour. What is the average speed (Km/hour) for the entire distance ?

Options

A. 63
B. `62 7/27`
C. `56 7/27`
D. `59 7/27`

Answer

To find the average speed of the man who travels different distances by various modes of transport, we will follow these steps:

### Step 1: Calculate Total Distance
The total distance traveled by the man is the sum of the distances traveled by each mode of transport.

- Distance by train = 600 km
- Distance by ship = 600 km
- Distance by aeroplane = 500 km
- Distance by car = 300 km

**Total Distance = 600 + 600 + 500 + 300 = 2000 km**

### Step 2: Calculate Time Taken for Each Mode of Transport
To find the total time taken, we will calculate the time taken for each mode of transport using the formula:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

1. **Time by Train:**
- Distance = 600 km
- Speed = 80 km/h
- Time = \( \frac{600}{80} = 7.5 \) hours

2. **Time by Ship:**
- Distance = 600 km
- Speed = 30 km/h
- Time = \( \frac{600}{30} = 20 \) hours

3. **Time by Aeroplane:**
- Distance = 500 km
- Speed = 400 km/h
- Time = \( \frac{500}{400} = 1.25 \) hours

4. **Time by Car:**
- Distance = 300 km
- Speed = 60 km/h
- Time = \( \frac{300}{60} = 5 \) hours

### Step 3: Calculate Total Time
Now, we will sum up all the times calculated above.

**Total Time = 7.5 + 20 + 1.25 + 5 = 33.75 hours**

### Step 4: Calculate Average Speed
Average speed is calculated using the formula:

\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

Substituting the values we have:

\[ \text{Average Speed} = \frac{2000 \text{ km}}{33.75 \text{ hours}} \]

### Step 5: Simplify the Average Speed Calculation
To simplify the calculation:

1. Multiply the numerator and denominator to avoid decimals:
- \( 2000 \div 33.75 = 2000 \times \frac{100}{3375} = \frac{200000}{3375} \)

2. Simplifying \( \frac{200000}{3375} \):
- Dividing both by 25 gives \( \frac{8000}{135} \)
- Further simplifying gives approximately \( 59.259 \) km/h.

### Final Result
Thus, the average speed for the entire distance is approximately **59.26 km/h**.