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Question

Consider an equilateral triangle ABC as given in the following diagram :

 



 

Two people start at the same time from points A and B with speeds 30 km per hour and 20 km per hour respectively, and move on the sides of the triangle in the clockwise direction. They meet each other for the first time at

The correct answer is
point A

This problem involves calculating when two people, starting from different points on an equilateral triangle and traveling at different speeds, will first meet. Let's solve this step-by-step.

Given:

  • The triangle ABC is an equilateral triangle.
  • The speeds of the two people are 30 km/hr and 20 km/hr, starting from points A and B respectively, moving in clockwise direction.

Objective:

Determine where the two people will first meet.

Solution:

  1. Calculate the relative speed of the two people as they are moving in the same direction:
    • Person at A moves at 30 km/hr.
    • Person at B moves at 20 km/hr.
    • Relative speed = 30 km/hr - 20 km/hr = 10 km/hr.
  2. Since they meet when the faster person (from A) catches up with the slower person (from B), we need to calculate when the faster person will complete one full lap and also position themselves at the starting point of the slower person.
  3. As they meet when either completes one full lap of the triangle, let's assume the side length of the triangle is \( s \). Therefore, the perimeter is \( 3s \).
  4. The time taken to complete one lap by the faster person moving at 30 km/hr is:
    • Time = \( \frac{3s}{30} \) hours.
  5. The slower person will also take the same time but being slower, will revisit the starting point naturally or meet at similar multiple of timings.
  6. Thus, they first meet again at their starting points simultaneously after the distance covered by each is exactly equal to the perimeter.

Therefore, the two people meet for the first time at point A.

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Important Questions from Relative Speed

  1. Ankur jogs on a circular track X at $1 \frac{2}{3}$ m/s and Mahima jogs on track Y at $2 \frac{1}{12}$ m/s. The total length of Tracks X and Y is 0.325 km. Ankur makes 9 rounds of track X in the same time Mahima makes 5 rounds of track Y. The time taken (in seconds) by Mahima to complete one round of track X is:
  2. Two places, A and B are 3710 kms from each other. A train leaves from A to B at the same time another train leaves B to A. The two trains meet at the end of 35 hours. If the train travelling from A to B travels 35 kmph faster than the other. Find the speed of the faster train. (In kmph)
  3. A truck, 1575 metres long is running at a speed of 109 km/hr. How many seconds will it take to cross a 1475 metres long train running in the same direction at a speed of 79 km/hr?
  4. A truck, 1600 metres long is running at a speed of 112 km/hr. How many seconds will it take to cross a 1500 metres long train running in the same direction at a speed of 82 km/hr?
  5. Two friends 10 km apart start running towards each other at speeds of 10 km/hr and 14 km/hr respectively. After how much time will they meet each other?
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