A person travels 600km by train at 80 km/hr, 800km by ship at 40km/hr 500km by aeroplane at 400km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance ?

Options

A. `65(5)/(123)` km/hr
B. 60km/hr
C. `60 (5)/(123)`km/hr
D. 62 km/hr

Answer

To find the average speed for the entire distance traveled by the person, we can follow these steps:

### Step 1: Calculate Total Distance
The total distance traveled is the sum of all the individual distances:
- Distance by train = 600 km
- Distance by ship = 800 km
- Distance by aeroplane = 500 km
- Distance by car = 100 km

Total Distance = 600 km + 800 km + 500 km + 100 km

**Calculation:**
Total Distance = 600 + 800 + 500 + 100 = 2000 km

### Step 2: Calculate Total Time
Next, we need to calculate the time taken for each segment of the journey using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

1. **Time by Train:**
- Distance = 600 km
- Speed = 80 km/hr
\[ \text{Time} = \frac{600}{80} = 7.5 \text{ hours} \]

2. **Time by Ship:**
- Distance = 800 km
- Speed = 40 km/hr
\[ \text{Time} = \frac{800}{40} = 20 \text{ hours} \]

3. **Time by Aeroplane:**
- Distance = 500 km
- Speed = 400 km/hr
\[ \text{Time} = \frac{500}{400} = 1.25 \text{ hours} \]

4. **Time by Car:**
- Distance = 100 km
- Speed = 50 km/hr
\[ \text{Time} = \frac{100}{50} = 2 \text{ hours} \]

**Total Time Calculation:**
Now, we sum all the times:
\[ \text{Total Time} = 7.5 + 20 + 1.25 + 2 \]

**Calculation:**
Total Time = 7.5 + 20 + 1.25 + 2 = 30.75 hours

### Step 3: Calculate Average Speed
The average speed is calculated using the formula:
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

**Calculation:**
\[ \text{Average Speed} = \frac{2000 \text{ km}}{30.75 \text{ hours}} \approx 65.57 \text{ km/hr} \]

### Final Answer
The average speed for the entire distance is approximately **65.57 km/hr**.

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