Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?

1. Break Down the Problem

To find out how many minutes the bus stops per hour, we need to determine the difference in time due to stoppages. We will use the speeds of the bus with and without considering stoppages.

2. Relevant Concepts

Let:

• Speed excluding stoppages (S₁) = 54 km/h
• Speed including stoppages (S₂) = 45 km/h

The time taken to travel a specific distance is directly affected by the speed. The time can be derived from the formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

3. Analysis and Detail

Let’s assume the bus travels for 1 hour (60 minutes).

• Distance traveled in 1 hour without stoppages: $D = S₁ \times 1 \, \text{hour} = 54 \, \text{km}$

• Time taken to travel the same distance including stoppages: $\text{Time with stoppages} = \frac{D}{S₂} = \frac{54 \, \text{km}}{45 \, \text{km/h}} = \frac{54}{45} \, \text{hours} = 1.2 \, \text{hours} = 1 \, \text{hour} + 12 \, \text{minutes}$

4. Verify and Summarize

• The bus takes 1.2 hours to travel the same distance, where it would normally take only 1 hour.

The difference in time is: $\text{Time lost due to stoppages} = 1.2 \, \text{hours} - 1 \, \text{hour} = 0.2 \, \text{hours} = 12 \, \text{minutes}$

Final Answer

The bus stops for 12 minutes per hour.