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Two cyclists start on a circular track from a given point but in opposite directions with speeds of 7 m/sec and 8 m/sec respectively. If the circumference of the circle is 300 metres, after what time will they meet at the starting point for the first time?
- a)20 sec
- b)100 sec
- c)300 sec
- d)200 sec
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two cyclists start on a circular track from a given point but in oppos...
S = D/T The times taken by the two cyclists to reach the starting point are 300/7 seconds and 300/8 seconds respectively. So, they will meet at the starting point after LCM(300/7, 300/8) = 300 seconds.
Most Upvoted Answer
Two cyclists start on a circular track from a given point but in oppos...
Given:
- Two cyclists start on a circular track from a given point.
- They are moving in opposite directions.
- The speed of the first cyclist is 7 m/sec.
- The speed of the second cyclist is 8 m/sec.
- The circumference of the circular track is 300 metres.
To find:
The time at which they will meet at the starting point for the first time.
Explanation:
When two objects move in opposite directions, they are moving towards each other. To find the time at which they meet, we need to calculate the time it takes for them to cover the total distance of the circular track.
Step 1: Calculate the relative speed
- The relative speed is the combined speed at which the two cyclists are moving towards each other.
- Since they are moving in opposite directions, we can add their speeds.
- Relative speed = Speed of cyclist 1 + Speed of cyclist 2 = 7 m/sec + 8 m/sec = 15 m/sec
Step 2: Calculate the time taken to cover the distance
- To find the time, we can use the formula: Time = Distance / Speed
- Distance = Circumference of the circular track = 300 metres
- Speed = Relative speed = 15 m/sec
- Time = 300 m / 15 m/sec = 20 sec
Step 3: Final Answer
- After 20 seconds, the two cyclists will meet at the starting point for the first time.
Conclusion:
The correct answer is option (a) 20 seconds.
- Two cyclists start on a circular track from a given point.
- They are moving in opposite directions.
- The speed of the first cyclist is 7 m/sec.
- The speed of the second cyclist is 8 m/sec.
- The circumference of the circular track is 300 metres.
To find:
The time at which they will meet at the starting point for the first time.
Explanation:
When two objects move in opposite directions, they are moving towards each other. To find the time at which they meet, we need to calculate the time it takes for them to cover the total distance of the circular track.
Step 1: Calculate the relative speed
- The relative speed is the combined speed at which the two cyclists are moving towards each other.
- Since they are moving in opposite directions, we can add their speeds.
- Relative speed = Speed of cyclist 1 + Speed of cyclist 2 = 7 m/sec + 8 m/sec = 15 m/sec
Step 2: Calculate the time taken to cover the distance
- To find the time, we can use the formula: Time = Distance / Speed
- Distance = Circumference of the circular track = 300 metres
- Speed = Relative speed = 15 m/sec
- Time = 300 m / 15 m/sec = 20 sec
Step 3: Final Answer
- After 20 seconds, the two cyclists will meet at the starting point for the first time.
Conclusion:
The correct answer is option (a) 20 seconds.
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Two cyclists start on a circular track from a given point but in opposite directions with speeds of 7 m/sec and 8 m/sec respectively. If the circumference of the circle is 300 metres, after what time will they meet at the starting point for the first time?a)20 secb)100 secc)300 secd)200 secCorrect answer is option 'C'. Can you explain this answer?
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