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A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops?
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A thief is running towards an airport which is 100 km away from him at...
Introduction:
In this problem, we are given the scenario of a thief trying to escape from the police. The thief is running towards an airport which is 100 km away from him at a speed of 10 km per hour. The police is at a distance of 600 km from the airport and chasing in a van at a speed of 120 km per hour. After 20 hours, the police van gets damaged and its speed reduces to 90 km per hour. We need to determine the speed at which the thief should run in order to escape the cops.
Calculating the time taken by the police to reach the airport:
The police is initially 600 km away from the airport and traveling at a speed of 120 km per hour. Therefore, the time taken by the police to reach the airport can be calculated as:
Time taken = Distance / Speed = 600 km / 120 km/hr = 5 hours
Calculating the distance covered by the thief:
The thief is running towards the airport at a speed of 10 km per hour for 20 hours. Therefore, the distance covered by the thief can be calculated as:
Distance covered = Speed × Time = 10 km/hr × 20 hr = 200 km
Calculating the remaining distance to be covered by the thief:
The remaining distance to be covered by the thief can be calculated by subtracting the distance covered by the thief from the total distance between the thief and the airport. Therefore,
Remaining distance = Total distance - Distance covered = 600 km - 200 km = 400 km
Calculating the time taken by the thief to cover the remaining distance:
Since the thief is running with an unknown speed, let's assume the speed of the thief is 'x' km per hour. Therefore, the time taken by the thief to cover the remaining distance can be calculated as:
Time taken = Distance / Speed = 400 km / x km/hr = 400/x hours
Calculating the total time taken by the police:
The police initially took 5 hours to reach the airport. After that, the police van got damaged and its speed reduced to 90 km per hour. Therefore, the total time taken by the police can be calculated as:
Total time taken = Time taken initially + Time taken after the van got damaged = 5 hours + 400/x hours
Equating the total time taken by the police and the thief:
Since the thief wants to escape the cops, the total time taken by the thief should be equal to or less than the total time taken by the police. Therefore, we can equate the two equations as follows:
20 hours + Distance covered by the thief / Speed of the thief ≤ 5 hours + 400/x hours
Simplifying the equation:
20 + 200 / x ≤ 5 + 400 / x
Calculating the speed of the thief:
To calculate the speed of the thief, we can cross multiply the equation and solve for 'x':
20x + 200 ≤ 5x + 400
15x ≤ 200
x ≤ 200 / 15
x ≤ 40/3
Conclusion:
Therefore, the thief should run at a speed of 40/3 km per hour or approximately 13.
In this problem, we are given the scenario of a thief trying to escape from the police. The thief is running towards an airport which is 100 km away from him at a speed of 10 km per hour. The police is at a distance of 600 km from the airport and chasing in a van at a speed of 120 km per hour. After 20 hours, the police van gets damaged and its speed reduces to 90 km per hour. We need to determine the speed at which the thief should run in order to escape the cops.
Calculating the time taken by the police to reach the airport:
The police is initially 600 km away from the airport and traveling at a speed of 120 km per hour. Therefore, the time taken by the police to reach the airport can be calculated as:
Time taken = Distance / Speed = 600 km / 120 km/hr = 5 hours
Calculating the distance covered by the thief:
The thief is running towards the airport at a speed of 10 km per hour for 20 hours. Therefore, the distance covered by the thief can be calculated as:
Distance covered = Speed × Time = 10 km/hr × 20 hr = 200 km
Calculating the remaining distance to be covered by the thief:
The remaining distance to be covered by the thief can be calculated by subtracting the distance covered by the thief from the total distance between the thief and the airport. Therefore,
Remaining distance = Total distance - Distance covered = 600 km - 200 km = 400 km
Calculating the time taken by the thief to cover the remaining distance:
Since the thief is running with an unknown speed, let's assume the speed of the thief is 'x' km per hour. Therefore, the time taken by the thief to cover the remaining distance can be calculated as:
Time taken = Distance / Speed = 400 km / x km/hr = 400/x hours
Calculating the total time taken by the police:
The police initially took 5 hours to reach the airport. After that, the police van got damaged and its speed reduced to 90 km per hour. Therefore, the total time taken by the police can be calculated as:
Total time taken = Time taken initially + Time taken after the van got damaged = 5 hours + 400/x hours
Equating the total time taken by the police and the thief:
Since the thief wants to escape the cops, the total time taken by the thief should be equal to or less than the total time taken by the police. Therefore, we can equate the two equations as follows:
20 hours + Distance covered by the thief / Speed of the thief ≤ 5 hours + 400/x hours
Simplifying the equation:
20 + 200 / x ≤ 5 + 400 / x
Calculating the speed of the thief:
To calculate the speed of the thief, we can cross multiply the equation and solve for 'x':
20x + 200 ≤ 5x + 400
15x ≤ 200
x ≤ 200 / 15
x ≤ 40/3
Conclusion:
Therefore, the thief should run at a speed of 40/3 km per hour or approximately 13.
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A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops?
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A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops?.
A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops?.
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A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops?, a detailed solution for A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops? has been provided alongside types of A thief is running towards an airport which is 100 km away from him at 10 km per hour police is at a distance of 600 km from the airport chasing in a van at 120 km per hour after 20 hours the police van got damaged and the speed was reduced to 90 km per hour. at that moment the theif had realised that Cops are chasing him at what speed this thief should run such that he escapes the cops? theory, EduRev gives you an
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