The driver of an ambulance sees a school bus 40 m ahead of him. After 20 second, the school bus is 60 metre behind. If the speed of the ambulance is 30 km/h, what is the speed of the school bus?

Options

A. 10 km/h
B. 12 km/h
C. 15 km/h
D. 22 km/h

Answer

To solve the problem step by step, we will analyze the information provided and apply the concept of relative speed.

### Step 1: Understand the initial and final positions
- Initially, the ambulance is 40 meters behind the school bus.
- After 20 seconds, the school bus is 60 meters behind the ambulance.

### Step 2: Calculate the distance covered by the ambulance
- The speed of the ambulance is given as 30 km/h.
- To convert this speed into meters per second, we use the conversion factor:
\[ 30 \text{ km/h} = \frac{30 \times 1000 \text{ m}}{3600 \text{ s}} = \frac{30000}{3600} \approx 8.33 \text{ m/s} \]

### Step 3: Calculate the distance traveled by the ambulance in 20 seconds
- Using the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
- The distance traveled by the ambulance in 20 seconds is:
\[ \text{Distance} = 8.33 \text{ m/s} \times 20 \text{ s} = 166.67 \text{ m} \]

### Step 4: Calculate the total distance between the ambulance and the school bus
- Initially, the ambulance was 40 meters behind the school bus.
- After 20 seconds, the school bus is now 60 meters behind the ambulance.
- Therefore, the total distance covered by the ambulance to reach this position is:
\[ \text{Total Distance} = 40 \text{ m} + 60 \text{ m} = 100 \text{ m} \]

### Step 5: Determine the distance covered by the school bus
- The distance covered by the school bus in the same time (20 seconds) can be calculated as:
\[ \text{Distance covered by the school bus} = \text{Distance traveled by the ambulance} - \text{Total Distance} \]
- Thus, the distance covered by the school bus is:
\[ \text{Distance} = 166.67 \text{ m} - 100 \text{ m} = 66.67 \text{ m} \]

### Step 6: Calculate the speed of the school bus
- Now, we can find the speed of the school bus using the formula:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{66.67 \text{ m}}{20 \text{ s}} \approx 3.33 \text{ m/s} \]
- To convert this speed back to km/h:
\[ 3.33 \text{ m/s} = 3.33 \times \frac{3600}{1000} \approx 12 \text{ km/h} \]

### Conclusion
The speed of the school bus is **12 km/h**.

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