Without any stoppage a person travels a cetain distance at an average speed 80 km/h and with stoppages he covers the same distance at an average speed of 60 km/h. How many minutes per hour does he stop ?

Answer

To solve the problem, we need to determine how many minutes per hour the person stops while traveling. We can do this using the formula related to average speed and time.

### Step-by-Step Solution:

1. **Define the Variables**:
- Let the distance traveled be \( D \) kilometers.
- Let the time taken without stoppage be \( T_1 \) hours.
- Let the time taken with stoppage be \( T_2 \) hours.

2. **Calculate Time Without Stoppage**:
- The average speed without stoppage is 80 km/h.
- Therefore, the time taken without stoppage can be calculated using the formula:
\[ T_1 = \frac{D}{80} \]

3. **Calculate Time With Stoppage**:
- The average speed with stoppage is 60 km/h.
- Therefore, the time taken with stoppage can be calculated using the formula:
\[ T_2 = \frac{D}{60} \]

4. **Determine the Time Stopped**:
- The time stopped is the difference between the time taken with stoppage and the time taken without stoppage:
\[ \text{Time Stopped} = T_2 - T_1 \]
- Substituting the values of \( T_1 \) and \( T_2 \):
\[ \text{Time Stopped} = \frac{D}{60} - \frac{D}{80} \]

5. **Find a Common Denominator**:
- The common denominator for 60 and 80 is 240. Therefore, we can rewrite the fractions:
\[ \text{Time Stopped} = \frac{4D}{240} - \frac{3D}{240} = \frac{D}{240} \]

6. **Calculate the Total Time with Stoppage**:
- The total time with stoppage is:
\[ T_2 = \frac{D}{60} \]

7. **Calculate the Stoppage Time as a Fraction of Total Time**:
- The fraction of time spent stopping is:
\[ \text{Fraction Stopped} = \frac{\text{Time Stopped}}{T_2} = \frac{\frac{D}{240}}{\frac{D}{60}} = \frac{1}{4} \]

8. **Convert the Fraction to Minutes per Hour**:
- Since there are 60 minutes in an hour, the time stopped per hour is:
\[ \text{Minutes Stopped} = \frac{1}{4} \times 60 = 15 \text{ minutes} \]

### Final Answer:
The person stops for **15 minutes per hour**.