Understanding Bus Stoppage Time: A Comprehensive Guide
Understanding the relationship between a bus's speed with and without stoppages is crucial for travelers and transportation planners. This guide explains the concept and provides a detailed method to calculate the bus stoppage time based on the bus's average speeds.
Introduction
Bus stoppage time refers to the period during which a bus is stationary during its journey. This time can significantly affect the overall travel duration and the perceived speed of the bus. Once these factors are understood, passengers can better plan their itineraries, and transportation companies can improve their services.
Problem Statement and Solution
In the given problem, we have two scenarios for a bus:
1. Speed without stoppages: 64 km/h
2. Speed including stoppages: 48 km/h
To find out how much time the bus stops per hour, we can use the following approach:
Define Variables: Let D be the constant distance covered by the bus in kilometers.Let T be the required stoppage time in minutes per hour. Set Up the Equation:
Without stoppages:
Speed Distance / Time
64 km/h D / T1
With stoppages:
48 km/h D / (T1 T)
Solve the Equations:T1 T / 60
48 D / (T / 60 T)
Simplify the equation to find T:
48 D / ((T 60T) / 60)
48 D / (61T / 60)
Multiply both sides by 60 to get:
2880 61D / T
T 2880 / 61
T ≈ 47.18 minutes
While this calculation provides an approximate answer, it can be simplified based on typical scenarios. Let's consider another example where the speed without stoppages is 54 km/h and including stoppages is 45 km/h.
Case Study: 54 km/h and 45 km/h
Let's calculate the bus's stoppage time for a 60-minute journey:
Speed without stoppages (D/H) 54 km/h
Speed with stoppages (D/H) 45 km/h
Difference in speeds 54 - 45 9 km/h
Time taken to cover 9 km without stoppages (T1):
T1 (9/54) * 60 10 minutes
Since 9 km is equivalent to 1/6 of the speed, the stoppage time is 1/5 of the hour:
Total stoppage time per hour 60/5 12 minutes
This indicates that the bus stops for approximately 12 minutes per hour.
Additional Calculations and Conversions
For a more precise calculation, consider an instance where the speed is measured in miles per hour. We know that:
1 mile 1.609344 km
For 54 km/h, the equivalent speed in miles per hour is calculated as:
54 km/h 54 / 1.609344 ≈ 33.56 miles/hour
The bus speed in miles during stoppages:
45 km/h 45 / 1.609344 ≈ 28.02 miles/hour
Time taken to cover 9 km with stoppages (T2):
T2 (9 * 60) / 54 * 1.609344 ≈ 22.72 minutes
Hence, the bus stops for approximately 22 minutes and 43 seconds per hour.
Conclusion
Understanding the concept of bus stoppage time is essential for optimizing travel plans and improving public transportation services. By using these calculations, transportation companies can better manage their schedules, while passengers can plan their journeys more effectively.