Excluding stoppages, the speed of a train is 60 km/h and including sto...
Understanding Train Speeds
When analyzing the problem, we have two types of speeds for the train:
- **Excluding Stoppages Speed:** 60 km/h
- **Including Stoppages Speed:** 50 km/h
Calculating Effective Speed Loss
The difference between these two speeds indicates the impact of stoppages:
- **Speed Difference:**
- 60 km/h (excluding stoppages) - 50 km/h (including stoppages)
- = 10 km/h
This difference represents the speed lost due to the time the train stops.
Determining Time Stopped
To find out how much time the train stops per hour, we use the following reasoning:
- **Time Calculation:**
- At a speed of 60 km/h, the train covers 60 kilometers in one hour.
- Since it effectively travels at 50 km/h including stoppages, it still covers 50 kilometers in that hour.
Time Stopped per Hour
Now, we need to calculate how long the train stops in that hour:
- **Distance lost due to stoppages:**
- 60 km (travelled without stoppages) - 50 km (travelled with stoppages) = 10 km
- **Time taken to cover 10 km at 60 km/h:**
- Time = Distance / Speed = 10 km / 60 km/h
- = 1/6 hour
To convert this into minutes:
- **Converting Hours to Minutes:**
- (1/6) hour × 60 minutes/hour = 10 minutes
However, since we want to know the time stopped in one hour, we need to consider the ratio of the total time:
- **Actual Time Stopped:**
- Since the speed including stoppages is 50 km/h, the time for actual travel is 50 km / 50 km/h = 1 hour.
Thus, in this hour, the train stops for:
- **Total Time Stopped:**
- 60 minutes - 50 minutes = 10 minutes
Upon reviewing the calculations, the correct answer should actually be that the train stops for **10 minutes per hour**. However, if there is an error in options, the time stopped can be interpreted as **12 minutes** if considering variations in calculation.
Ultimately, option **'B' (12 minutes)** appears to be a miscalculation. The accurate stopping time is confirmed to be **10 minutes**.
Excluding stoppages, the speed of a train is 60 km/h and including sto...
Due to stoppages, train covers 10 km less.
Time taken to cover 10 km