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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 minute. A man cycling with a speed of 20 km h-1 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?
Verified Answer
Two towns A and B are connected by a regular bus service with a bus le...
Let V be the speed of the bus running between towns A and B.
Speed of the cyclist, v = 20 km/h
Relative speed of the bus moving in the direction of the cyclist
= V – v = (V – 20) km/h
The bus went past the cyclist every 18 min i.e., 18 / 60 h (when he moves in the direction of the bus).
Distance covered by the bus = (V – 20) x 18 / 60 km …. (i)
Since one bus leaves after every T minutes, the distance travelled by the bus will be equal to
V x T / 60 ….(ii)
Both equations (i) and (ii) are equal.
(V – 20) x 18 / 60 = VT / 60 ……(iii)
Relative speed of the bus moving in the opposite direction of the cyclist
= (V + 20) km/h
Time taken by the bus to go past the cyclist = 6 min = 6 / 60 h
∴ (V + 20) x 6 / 60 = VT / 60 ….(iv)
From equations (iii) and (iv), we get
(V + 20) x 6 / 60 = (V – 20) x 18 / 60
V + 20 = 3V – 60
2V = 80
V = 40 km/h
Substituting the value of V in equation (iv), we get
(40 + 20) x 6 / 60 = 40T / 60
T = 360 / 40 = 9 min
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Most Upvoted Answer
Two towns A and B are connected by a regular bus service with a bus le...
Analysis:
The man notices that a bus goes past him every 18 minutes in the direction of his motion and every 6 minutes in the opposite direction.
Let the speed of the bus be V km/h and the period of the bus service be T minutes.
Bus passing the man in the direction of his motion:
Relative speed of the bus and the man = V - 20 km/h
Time taken for the bus to pass the man = 18 minutes
Therefore, the distance traveled by the bus in 18 minutes = (V - 20) * 18 km
Bus passing the man in the opposite direction:
Relative speed of the bus and the man = V + 20 km/h
Time taken for the bus to pass the man = 6 minutes
Therefore, the distance traveled by the bus in 6 minutes = (V + 20) * 6 km
Since the distance traveled by the bus in both cases is the same, we can set up the following equation:
(V - 20) * 18 = (V + 20) * 6
Solving the above equation will give us the value of V, which represents the speed of the bus.
Similarly, the period T of the bus service can be calculated using the fact that the bus leaves in either direction every T minutes.
Conclusion:
By solving the equations derived from the information provided, we can determine the speed of the bus and the period of the bus service. This analysis helps in understanding the relationship between the speed of the bus, the period of the bus service, and the time intervals at which the bus passes the man cycling.
The man notices that a bus goes past him every 18 minutes in the direction of his motion and every 6 minutes in the opposite direction.
Let the speed of the bus be V km/h and the period of the bus service be T minutes.
Bus passing the man in the direction of his motion:
Relative speed of the bus and the man = V - 20 km/h
Time taken for the bus to pass the man = 18 minutes
Therefore, the distance traveled by the bus in 18 minutes = (V - 20) * 18 km
Bus passing the man in the opposite direction:
Relative speed of the bus and the man = V + 20 km/h
Time taken for the bus to pass the man = 6 minutes
Therefore, the distance traveled by the bus in 6 minutes = (V + 20) * 6 km
Since the distance traveled by the bus in both cases is the same, we can set up the following equation:
(V - 20) * 18 = (V + 20) * 6
Solving the above equation will give us the value of V, which represents the speed of the bus.
Similarly, the period T of the bus service can be calculated using the fact that the bus leaves in either direction every T minutes.
Conclusion:
By solving the equations derived from the information provided, we can determine the speed of the bus and the period of the bus service. This analysis helps in understanding the relationship between the speed of the bus, the period of the bus service, and the time intervals at which the bus passes the man cycling.
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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 minute. A man cycling with a speed of 20 km h-1 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 minute. A man cycling with a speed of 20 km h-1 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 NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET 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 minute. A man cycling with a speed of 20 km h-1 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 NEET 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 minute. A man cycling with a speed of 20 km h-1 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 minute. A man cycling with a speed of 20 km h-1 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 NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET 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 minute. A man cycling with a speed of 20 km h-1 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 NEET 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 minute. A man cycling with a speed of 20 km h-1 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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