Speed of a bus is 45 km/h. If it stops for a few minutes in an hour then its average speed becomes 42 km/h. Find out the time duration it stops for in an hour.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the given information
- The speed of the bus without stopping is 45 km/h.
- The average speed of the bus after stopping for a few minutes is 42 km/h.

### Step 2: Calculate the distance covered without stopping
In one hour, if the bus travels at 45 km/h, the distance covered without stopping is:
\[ \text{Distance} = \text{Speed} \times \text{Time} = 45 \, \text{km/h} \times 1 \, \text{hour} = 45 \, \text{km} \]

### Step 3: Calculate the distance covered with stops
If the average speed of the bus is 42 km/h over the same duration of 1 hour, the distance covered with stops is:
\[ \text{Distance} = \text{Average Speed} \times \text{Time} = 42 \, \text{km/h} \times 1 \, \text{hour} = 42 \, \text{km} \]

### Step 4: Determine the distance lost due to stopping
The difference in distance due to stopping is:
\[ \text{Distance lost} = \text{Distance without stops} - \text{Distance with stops} = 45 \, \text{km} - 42 \, \text{km} = 3 \, \text{km} \]

### Step 5: Calculate the time taken to cover the lost distance
The speed of the bus is 45 km/h. To find the time taken to cover the lost distance of 3 km, we use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{3 \, \text{km}}{45 \, \text{km/h}} = \frac{1}{15} \, \text{hours} \]

### Step 6: Convert the time from hours to minutes
To convert the time from hours to minutes, we multiply by 60:
\[ \text{Time in minutes} = \frac{1}{15} \, \text{hours} \times 60 \, \text{minutes/hour} = 4 \, \text{minutes} \]

### Conclusion
The bus stops for **4 minutes** in an hour.

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