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Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?
Most Upvoted Answer
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
- 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
Community Answer
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???
Velocity of bus is two times that of cyclist???
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Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?
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Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?.
Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?.
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Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road?, a detailed solution for Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road? has been provided alongside types of Two towns A and B are connected by a regular bus service with a bus leaving in either direction every T minutes. A man cycling with a speed of in the direction A to B notices that a bus goes past him every 18 min in the direction of his motion, and every 6 min in the opposite direction. What is the period T of the bus service and with what speed (assumed constant) do the buses ply on the road? theory, EduRev gives you an
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