Two towns A and B are connected by a regular bus service with a bus le...
Given information:
- A man cycling from town A to town B notices that a bus passes him every 18 minutes.
- A bus passing in the opposite direction is noticed by the man every 6 minutes.
Objective:
- Determine the period T of the bus service.
- Determine the speed at which the buses ply on the road.
Assumptions:
- The man's cycling speed is constant.
- The bus speed is constant.
Approach:
1. Understand the relationship between the time taken for a bus to pass the man and the time interval between buses.
2. Use this relationship to calculate the period T of the bus service.
3. Calculate the speed of the buses using the formula: Speed = Distance/Time.
Solution:
1. Relationship between time taken for a bus to pass the man and time interval between buses:
- When the man cycles in the direction of the bus, he notices a bus passing him every 18 minutes.
- This means that in 18 minutes, the bus catches up to the man and passes him.
- Therefore, the time taken for a bus to pass the man is 18 minutes.
- When the man cycles in the opposite direction of the bus, he notices a bus passing him every 6 minutes.
- This means that in 6 minutes, the bus catches up to the man and passes him.
- Therefore, the time taken for a bus to pass the man is 6 minutes.
2. Calculating the period T of the bus service:
- Let's assume the distance between town A and town B is D.
- When the man cycles in the direction of the bus, the relative speed between the man and the bus is the sum of their speeds.
- Therefore, the time taken for the bus to pass the man is D/(man's speed + bus's speed).
- According to the given information, this time is 18 minutes.
- Similarly, when the man cycles in the opposite direction of the bus, the relative speed between the man and the bus is the difference of their speeds.
- Therefore, the time taken for the bus to pass the man is D/(bus's speed - man's speed).
- According to the given information, this time is 6 minutes.
- Equating the two expressions for the time taken:
D/(man's speed + bus's speed) = D/(bus's speed - man's speed)
- Solving this equation will give us the value of the period T.
3. Calculating the speed of the buses:
- Once we have the value of the period T, we can calculate the speed of the buses using the formula: Speed = Distance/Time.
- The distance between town A and town B (D) will be the same in both cases.
- We can use the value of D and the calculated value of T to determine the speed of the buses.
Summary:
- The period T of the bus service can be calculated by equating the time taken for the bus to pass the man in both directions.
- The speed of the buses can be calculated using the formula: Speed = Distance/Time.
- The distance between town A and town B (D) is a common factor in both calculations.
- By solving the equation and substituting the value of D, we can
Two towns A and B are connected by a regular bus service with a bus le...
T=9 MINS
Velocity of bus is two times that of cyclist???
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