It is 260 km from Patna to Ranchi by air and 320 km by road.an aeroplane takes 30 minutes to go from Patna to Ranchi whereas a delux bus takes 8 hours. a.Find the verge speed of the plane. b.Find the verage speed of the bus. C. Find the average velocity of the plane. d. Find the average velocity of the bus.

Explanation

To solve the problem step by step, we will break it down into parts as per the requirements of the question.

### Step 1: Find the average speed of the plane.

**Formula for average speed:**
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

**Given:**
- Distance traveled by the plane = 260 km
- Time taken by the plane = 30 minutes = 0.5 hours

**Calculation:**
\[ \text{Average Speed of Plane} = \frac{260 \text{ km}}{0.5 \text{ hours}} = 520 \text{ km/h} \]

### Step 2: Find the average speed of the bus.

**Given:**
- Distance traveled by the bus = 320 km
- Time taken by the bus = 8 hours

**Calculation:**
\[ \text{Average Speed of Bus} = \frac{320 \text{ km}}{8 \text{ hours}} = 40 \text{ km/h} \]

### Step 3: Find the average velocity of the plane.

**Average velocity is defined as:**
\[ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Time}} \]

**For the plane:**
- Displacement (straight line distance from Patna to Ranchi) = 260 km
- Time taken = 0.5 hours

**Calculation:**
\[ \text{Average Velocity of Plane} = \frac{260 \text{ km}}{0.5 \text{ hours}} = 520 \text{ km/h} \]

### Step 4: Find the average velocity of the bus.

**For the bus:**
- Displacement = 260 km (same as the plane since it is the straight-line distance)
- Time taken = 8 hours

**Calculation:**
\[ \text{Average Velocity of Bus} = \frac{260 \text{ km}}{8 \text{ hours}} = 32.5 \text{ km/h} \]

### Summary of Results:
- Average Speed of Plane = 520 km/h
- Average Speed of Bus = 40 km/h
- Average Velocity of Plane = 520 km/h
- Average Velocity of Bus = 32.5 km/h

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