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Umapati and Virendranath take 21 minutes and 28 minutes respectively to cover a certain distance L. If they start from two points on a highway which are at a distance of 3L and move towards each other, how many minutes do they take to meet?

Question

Umapati and Virendranath take 21 minutes and 28 minutes respectively to cover a certain distance L. If they start from two points on a highway which are at a distance of 3L and move towards each other, how many minutes do they take to meet?

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Solution

To solve this problem, we need to find out how fast Umapati and Virendranath are moving.

  1. First, we calculate their speeds. Speed is distance divided by time. So, Umapati's speed is L/21 and Virendranath's speed is L/28.

  2. When two objects are moving towards each other, their relative speed is the sum of their individual speeds. So, the relative speed of Umapati and Virendranath is L/21 + L/28.

  3. To simplify this, we find a common denominator for 21 and 28, which is 588. So, their relative speed is 28L/588 + 21L/588 = 49L/588 = L/12.

  4. Now, we know their relative speed and the distance they need to cover, which is 3L. Time is distance divided by speed, so the time they take to meet is 3L / (L/12) = 36 minutes.

So, Umapati and Virendranath will meet after 36 minutes.

This problem has been solved

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