A bus starts running with the initial speed of 21km/hr and its speed increases every hour by 3 km/hr. How many hours will it take to cover a distance of 252 km?

Options

A. 3
B. 5
C. 8
D. 10

Answer

To solve the problem step by step, we will analyze the situation of the bus and its speed incrementally.

### Step 1: Understand the speed of the bus
The bus starts with an initial speed of 21 km/hr and increases its speed by 3 km/hr every hour.

### Step 2: Determine the speed for each hour
- **Hour 1:** Speed = 21 km/hr
- **Hour 2:** Speed = 21 + 3 = 24 km/hr
- **Hour 3:** Speed = 24 + 3 = 27 km/hr
- **Hour 4:** Speed = 27 + 3 = 30 km/hr
- **Hour 5:** Speed = 30 + 3 = 33 km/hr
- **Hour 6:** Speed = 33 + 3 = 36 km/hr
- **Hour 7:** Speed = 36 + 3 = 39 km/hr
- **Hour 8:** Speed = 39 + 3 = 42 km/hr
- **Hour 9:** Speed = 42 + 3 = 45 km/hr
- **Hour 10:** Speed = 45 + 3 = 48 km/hr

### Step 3: Calculate the distance covered in each hour
The distance covered in each hour can be calculated as follows:
- **Hour 1:** Distance = 21 km
- **Hour 2:** Distance = 24 km
- **Hour 3:** Distance = 27 km
- **Hour 4:** Distance = 30 km
- **Hour 5:** Distance = 33 km
- **Hour 6:** Distance = 36 km
- **Hour 7:** Distance = 39 km
- **Hour 8:** Distance = 42 km
- **Hour 9:** Distance = 45 km
- **Hour 10:** Distance = 48 km

### Step 4: Sum the distances to find the total distance covered
We need to find out how many hours it takes to cover a total distance of 252 km. We will sum the distances hour by hour until we reach or exceed 252 km.

- After 1 hour: 21 km
- After 2 hours: 21 + 24 = 45 km
- After 3 hours: 45 + 27 = 72 km
- After 4 hours: 72 + 30 = 102 km
- After 5 hours: 102 + 33 = 135 km
- After 6 hours: 135 + 36 = 171 km
- After 7 hours: 171 + 39 = 210 km
- After 8 hours: 210 + 42 = 252 km

### Step 5: Conclusion
The bus will take **8 hours** to cover the distance of 252 km.