Excluding stoppages, the speed of a bus is 54 km per hour. Including stoppages, it is 45 km per hour. What is the stoppage time of the bus in minutes per hour?

To find the stoppage time of the bus in minutes per hour, let's go through the problem step by step.

### Step 1: Define Variables
- **Speed without stoppages** = 54 km/h
- **Speed with stoppages** = 45 km/h

### Step 2: Calculate Time Taken for 1 Hour of Travel Without Stoppages
In 1 hour, without stoppages, the bus covers:
\[ 54 \text{ km} \]

### Step 3: Calculate Time Taken for 1 Hour of Travel With Stoppages
In 1 hour, with stoppages, the bus covers:
\[ 45 \text{ km} \]

### Step 4: Determine the Distance Lost Due to Stoppages
The distance lost due to stoppages is the difference between the distance the bus would cover without stoppages and the distance it actually covers with stoppages:
\[ \text{Distance lost} = 54 \text{ km} - 45 \text{ km} = 9 \text{ km} \]

### Step 5: Calculate the Time Equivalent of the Distance Lost
To calculate how much time was lost due to the stoppages, we need to find out how long it would take to cover the 9 km that was not covered due to stoppages, using the speed of 54 km/h (which is the speed without stoppages).

Time taken to cover 9 km:
\[
\text{Time lost} = \frac{9 \text{ km}}{54 \text{ km/h}} = \frac{1}{6} \text{ hours}
\]

### Step 6: Convert Time Lost to Minutes
Now, convert \(\frac{1}{6}\) hours into minutes:
\[
\frac{1}{6} \text{ hours} \times 60 \text{ minutes/hour} = 10 \text{ minutes}
\]

### Final Answer:
The stoppage time of the bus is **10 minutes per hour**.

Would you like further details or have any questions?

### Follow-up Questions:
1. How do you calculate average speed when stoppages are involved?
2. What would the stoppage time be if the bus's speed without stoppages was 60 km/h and with stoppages was 50 km/h?
3. If the bus had 15 minutes of stoppage time per hour, what would its effective speed be?
4. How does the ratio of speeds with and without stoppages affect the stoppage time?
5. Can we use the same method to calculate stoppage time for different distances?
6. How would a 5-minute increase in stoppage time affect the overall journey duration?
7. What is the relationship between speed, distance, and time in this context?
8. How would a decrease in speed without stoppages impact the stoppage time?

**Tip:** Always double-check the units when converting time or speed to ensure accurate calculations.

Learn how to calculate the stoppage time of a bus per hour using speed, distance, and time concepts. This problem involves finding the difference in speed due to stoppages and converting it to minutes per hour. Suitable for students in Grades 6-8.

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