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A police officer is 110 meter behind a thief. The officer runs 21 meters and thief runs 14 meters in a minute. In what time the officer will catch the thief ?
- a)15.3/7 minutes
- b)15.5/7 minutes
- c)15.1/7 minutes
- d)16.3/7 minutes
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A police officer is 110 meter behind a thief. The officer runs 21 mete...
let the thief covers x more distance before get caught, so officer have to cover 110+x in the same time in which thief covers x distance ,
x/14 = (110 +x)/21, x = 220 so time = 330/21 = 110/7 = 15.5/7 minutes
x/14 = (110 +x)/21, x = 220 so time = 330/21 = 110/7 = 15.5/7 minutes
Most Upvoted Answer
A police officer is 110 meter behind a thief. The officer runs 21 mete...
To solve this problem, we can use the concept of relative speed. Let's break down the solution into steps:
Step 1: Calculate the relative speed
The relative speed between the police officer and the thief is the difference between their individual speeds. In this case, the police officer runs 21 meters per minute and the thief runs 14 meters per minute. Therefore, the relative speed is 21 - 14 = 7 meters per minute.
Step 2: Calculate the distance between the police officer and the thief
Given that the police officer is 110 meters behind the thief, we need to calculate the distance that needs to be covered by the police officer to catch up with the thief.
Distance = 110 meters
Step 3: Calculate the time required to catch the thief
Using the formula, Time = Distance/Speed, we can calculate the time required for the police officer to catch the thief.
Time = Distance/Relative Speed
Time = 110 meters/7 meters per minute
Simplifying this equation, we get:
Time = 15.7142857 minutes
Step 4: Convert the time to minutes and seconds
Since the question asks for the answer in minutes and seconds, we need to convert the decimal part of the time to seconds.
Decimal part = 0.7142857
Seconds = Decimal part * 60
Seconds = 0.7142857 * 60
Seconds = 42.857142 seconds
Rounding this to the nearest whole number, we get:
Seconds = 43 seconds
Therefore, the time required for the police officer to catch the thief is approximately 15 minutes and 43 seconds.
The correct answer is option 'B', which states 15.5/7 minutes.
Step 1: Calculate the relative speed
The relative speed between the police officer and the thief is the difference between their individual speeds. In this case, the police officer runs 21 meters per minute and the thief runs 14 meters per minute. Therefore, the relative speed is 21 - 14 = 7 meters per minute.
Step 2: Calculate the distance between the police officer and the thief
Given that the police officer is 110 meters behind the thief, we need to calculate the distance that needs to be covered by the police officer to catch up with the thief.
Distance = 110 meters
Step 3: Calculate the time required to catch the thief
Using the formula, Time = Distance/Speed, we can calculate the time required for the police officer to catch the thief.
Time = Distance/Relative Speed
Time = 110 meters/7 meters per minute
Simplifying this equation, we get:
Time = 15.7142857 minutes
Step 4: Convert the time to minutes and seconds
Since the question asks for the answer in minutes and seconds, we need to convert the decimal part of the time to seconds.
Decimal part = 0.7142857
Seconds = Decimal part * 60
Seconds = 0.7142857 * 60
Seconds = 42.857142 seconds
Rounding this to the nearest whole number, we get:
Seconds = 43 seconds
Therefore, the time required for the police officer to catch the thief is approximately 15 minutes and 43 seconds.
The correct answer is option 'B', which states 15.5/7 minutes.
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