Two points A and B are rically opposite points on a circular road of c...
Problem statement: A cyclist started from point A and made three rounds on a circular road of circumference 12 km. He made the first round with a speed of 12 kmph and decreased his speed by 3 kmph for every round. What is the interval between the first time he passes through B and the third time he passes through B?
Solution:
- Calculate the time taken for each round:
- For the first round, the speed of the cyclist is 12 kmph.
- Therefore, the time taken to complete one round is 1 hour (12/12).
- For the second round, the speed of the cyclist is 9 kmph.
- Therefore, the time taken to complete one round is 4/3 hours (12/9).
- For the third round, the speed of the cyclist is 6 kmph.
- Therefore, the time taken to complete one round is 2 hours (12/6).
- Calculate the time taken to pass through point B:
- For the first round, the cyclist passes through point B after 1/3 hour (1/3 x 12 = 4 km).
- For the second round, the cyclist passes through point B after 1 + 4/3 = 7/3 hours (7/3 x 9 = 21 km).
- For the third round, the cyclist passes through point B after 2 + 4/3 = 10/3 hours (10/3 x 6 = 20 km).
- Calculate the interval between the first and third time the cyclist passes through point B:
- The cyclist passes through point B for the first time after 1/3 hour.
- The cyclist passes through point B for the third time after 10/3 hours.
- Therefore, the interval between the first and third time the cyclist passes through point B is 10/3 - 1/3 = 3 hours.
- Convert hours to minutes: 3 x 60 = 180 minutes.
- Convert minutes to seconds: 180 x 60 = 10,800 seconds.
- Therefore, the interval between the first and third time the cyclist passes through point B is 10,800 seconds or 100 minutes (rounded to the nearest minute).
Therefore, the interval between the first and third time the cyclist passes through point B is 100.
Two points A and B are rically opposite points on a circular road of c...