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The distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph, while the other man travelled with varying speeds. In the first hour, his speed was 2 kmph, in the second hour, it was 2.5 kmph, in the third hour, it was 3 kmph and so on. When will they meet each other?
- a)7 hours
- b)10 hours
- c)35 km from A
- d)Mid-way between A and B
- e)Cannot be determined
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The distance between A and B is 72 km. Two men started walking from A...
Problem Analysis:
The two men start simultaneously from points A and B, respectively. The person who started from point A has a uniform speed of 4 kmph. The other man, however, has a varying speed, starting at 2 kmph and increasing by 0.5 kmph every hour. We need to find the time taken by both the men to meet each other.
Solution:
To solve the problem, we can use the formula:
Time taken = Distance/Relative Speed
Relative Speed is the difference between the speeds of the two men.
Let's assume that the two men meet after 't' hours at a point 'x' km from point A. Then, the distance covered by the man starting from A in 't' hours is 4t km, and the distance covered by the other man is:
2 kmph × 1 hour + 2.5 kmph × 1 hour + 3 kmph × 1 hour + ... (up to t hours)
= (2 + 2.5 + 3 + ... t) km
= t(2 + t/2) km (using the formula for sum of an arithmetic series)
Therefore, the distance between A and x is 4t km, and the distance between B and x is 72 - 4t km. Hence, we get the following equation:
4t + t(2 + t/2) = 72
Simplifying the above equation, we get:
t² + 8t - 72 = 0
Solving the quadratic equation, we get:
t = 6 or t = -12
Since t is the time taken, it cannot be negative. Therefore, t = 6.
This means that the two men meet each other after 6 hours of walking. To find the point where they meet, we substitute t = 6 in the equation for the distance covered by the other man:
Distance covered by the other man in 6 hours = 6(2 + 6/2) km = 27 km.
Therefore, the two men meet at a point which is 27 km from point A and 45 km from point B. This is exactly halfway between A and B.
Option (d) is the correct answer.
Final Answer: The two men meet each other after 6 hours of walking at a point which is halfway between A and B.
The two men start simultaneously from points A and B, respectively. The person who started from point A has a uniform speed of 4 kmph. The other man, however, has a varying speed, starting at 2 kmph and increasing by 0.5 kmph every hour. We need to find the time taken by both the men to meet each other.
Solution:
To solve the problem, we can use the formula:
Time taken = Distance/Relative Speed
Relative Speed is the difference between the speeds of the two men.
Let's assume that the two men meet after 't' hours at a point 'x' km from point A. Then, the distance covered by the man starting from A in 't' hours is 4t km, and the distance covered by the other man is:
2 kmph × 1 hour + 2.5 kmph × 1 hour + 3 kmph × 1 hour + ... (up to t hours)
= (2 + 2.5 + 3 + ... t) km
= t(2 + t/2) km (using the formula for sum of an arithmetic series)
Therefore, the distance between A and x is 4t km, and the distance between B and x is 72 - 4t km. Hence, we get the following equation:
4t + t(2 + t/2) = 72
Simplifying the above equation, we get:
t² + 8t - 72 = 0
Solving the quadratic equation, we get:
t = 6 or t = -12
Since t is the time taken, it cannot be negative. Therefore, t = 6.
This means that the two men meet each other after 6 hours of walking. To find the point where they meet, we substitute t = 6 in the equation for the distance covered by the other man:
Distance covered by the other man in 6 hours = 6(2 + 6/2) km = 27 km.
Therefore, the two men meet at a point which is 27 km from point A and 45 km from point B. This is exactly halfway between A and B.
Option (d) is the correct answer.
Final Answer: The two men meet each other after 6 hours of walking at a point which is halfway between A and B.
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Community Answer
The distance between A and B is 72 km. Two men started walking from A...
Let x and y be the persons who started from A and B, respectively.
Mid-way between A and B means 36 km from A and B both. x will take 9 hours to reach the mid-point. In 9 hours, y will also cover 2 + 2.5 + 3 + 3.5 + 4 + 4.5 + 5 + 5.5 + 6 = 36 km. Thus, y will also reach the mid-point at the same time.
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The distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph, while the other man travelled with varying speeds. In the first hour, his speed was 2 kmph, in the second hour, it was 2.5 kmph, in the third hour, it was 3 kmph and so on. When will they meet each other?a)7 hoursb)10 hoursc)35 km from Ad)Mid-way between A and Be)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?
Question Description
The distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph, while the other man travelled with varying speeds. In the first hour, his speed was 2 kmph, in the second hour, it was 2.5 kmph, in the third hour, it was 3 kmph and so on. When will they meet each other?a)7 hoursb)10 hoursc)35 km from Ad)Mid-way between A and Be)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph, while the other man travelled with varying speeds. In the first hour, his speed was 2 kmph, in the second hour, it was 2.5 kmph, in the third hour, it was 3 kmph and so on. When will they meet each other?a)7 hoursb)10 hoursc)35 km from Ad)Mid-way between A and Be)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph, while the other man travelled with varying speeds. In the first hour, his speed was 2 kmph, in the second hour, it was 2.5 kmph, in the third hour, it was 3 kmph and so on. When will they meet each other?a)7 hoursb)10 hoursc)35 km from Ad)Mid-way between A and Be)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?.
The distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph, while the other man travelled with varying speeds. In the first hour, his speed was 2 kmph, in the second hour, it was 2.5 kmph, in the third hour, it was 3 kmph and so on. When will they meet each other?a)7 hoursb)10 hoursc)35 km from Ad)Mid-way between A and Be)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph, while the other man travelled with varying speeds. In the first hour, his speed was 2 kmph, in the second hour, it was 2.5 kmph, in the third hour, it was 3 kmph and so on. When will they meet each other?a)7 hoursb)10 hoursc)35 km from Ad)Mid-way between A and Be)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The distance between A and B is 72 km. Two men started walking from A and B at the same time towards each other. The person who started from A travelled uniformly with average speed 4 kmph, while the other man travelled with varying speeds. In the first hour, his speed was 2 kmph, in the second hour, it was 2.5 kmph, in the third hour, it was 3 kmph and so on. When will they meet each other?a)7 hoursb)10 hoursc)35 km from Ad)Mid-way between A and Be)Cannot be determinedCorrect answer is option 'D'. Can you explain this answer?.
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