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Amir and Akbar enter a circular jogging track of length 300 m. They start at the same point running in opposite directions at the speeds of 10 m/s and 15 m/s respectively. How much distance would Akbar have covered by the time they both meet for the 30th time?
- a)3.6 km
- b)5.4 km
- c)2.4 km
- d)4.8 km
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Amir and Akbar enter a circular jogging track of length 300 m. They st...
The length of the circular track is 300 m.
Relative speed of Akbar and Amir = 10 + 15 = 25 m/s
Relative speed of Akbar and Amir = 10 + 15 = 25 m/s
Now, the distance between them is 300 m and they are running in opposite directions.
They will meet again after 12 s.
They will meet for the 30th time after 12 * 30 = 360 s
Distance covered by Akbar when he meets Amir for the 30th time = 15 x 360 = 5400 m = 5.4 km
Hence, option 2.
Most Upvoted Answer
Amir and Akbar enter a circular jogging track of length 300 m. They st...
To solve this problem, let's first calculate the time it takes for Amir and Akbar to meet for the first time.
Let the time taken for them to meet for the first time be t seconds.
The distance covered by Amir in t seconds = speed * time = 10 * t meters
The distance covered by Akbar in t seconds = speed * time = 15 * t meters
Since they are running in opposite directions, the sum of the distances covered by both of them should be equal to the length of the track, which is 300 meters.
So, 10t + 15t = 300
Simplifying the equation, we get:
25t = 300
t = 12 seconds
Therefore, it takes 12 seconds for Amir and Akbar to meet for the first time.
Now, let's calculate the time it takes for them to meet for the second time.
Since they are running in opposite directions, the relative speed between them is the sum of their individual speeds, which is 10 + 15 = 25 m/s.
The time taken for them to meet for the second time is given by:
Distance / Relative speed = 300 / 25 = 12 seconds
Similarly, we can calculate the time taken for them to meet for the third, fourth, and subsequent times. We observe that the time taken for them to meet for each subsequent time is constant and equal to 12 seconds.
Now, to calculate the distance covered by Akbar by the time they both meet for the 30th time, we can use the formula:
Distance = Speed * Time
The speed of Akbar is 15 m/s.
The time taken for them to meet for the 30th time is 12 seconds.
Therefore, the distance covered by Akbar = 15 * 12 = 180 meters.
Since 1 kilometer = 1000 meters, the distance covered by Akbar in kilometers = 180 / 1000 = 0.18 kilometers.
By the time they both meet for the 30th time, Akbar would have covered a distance of 0.18 kilometers.
Therefore, the correct answer is option B) 5.4 km.
Let the time taken for them to meet for the first time be t seconds.
The distance covered by Amir in t seconds = speed * time = 10 * t meters
The distance covered by Akbar in t seconds = speed * time = 15 * t meters
Since they are running in opposite directions, the sum of the distances covered by both of them should be equal to the length of the track, which is 300 meters.
So, 10t + 15t = 300
Simplifying the equation, we get:
25t = 300
t = 12 seconds
Therefore, it takes 12 seconds for Amir and Akbar to meet for the first time.
Now, let's calculate the time it takes for them to meet for the second time.
Since they are running in opposite directions, the relative speed between them is the sum of their individual speeds, which is 10 + 15 = 25 m/s.
The time taken for them to meet for the second time is given by:
Distance / Relative speed = 300 / 25 = 12 seconds
Similarly, we can calculate the time taken for them to meet for the third, fourth, and subsequent times. We observe that the time taken for them to meet for each subsequent time is constant and equal to 12 seconds.
Now, to calculate the distance covered by Akbar by the time they both meet for the 30th time, we can use the formula:
Distance = Speed * Time
The speed of Akbar is 15 m/s.
The time taken for them to meet for the 30th time is 12 seconds.
Therefore, the distance covered by Akbar = 15 * 12 = 180 meters.
Since 1 kilometer = 1000 meters, the distance covered by Akbar in kilometers = 180 / 1000 = 0.18 kilometers.
By the time they both meet for the 30th time, Akbar would have covered a distance of 0.18 kilometers.
Therefore, the correct answer is option B) 5.4 km.
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Amir and Akbar enter a circular jogging track of length 300 m. They start at the same point running in opposite directions at the speeds of 10 m/s and 15 m/s respectively. How much distancewould Akbar have covered by the time they both meet for the 30th time?a)3.6 kmb)5.4 kmc)2.4 kmd)4.8 kmCorrect answer is option 'B'. Can you explain this answer?
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