Multiple choice

Two athletes, Alex and Bob, start running simultaneously from a certain point on a circular track of length 800 m in opposite directions with speeds in the ratio 5 : 3. Which of the following gives a possible value of the distance (in m) of the starting point from the point on the track where their fourth meeting takes place?

  1. 100

  2. 200

  3. 300

  4. 400
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For opposite directions, they meet at points dividing the track in ratio of their speeds. Ratio 5:3 means they meet at points dividing the 800m track into 8 parts (100m each). The meetings occur at 5/8, 10/8, 15/8, 20/8 of the track. 20/8 = 2.5 laps. The distance from the start is 0.5 * 800 = 400m.

AI explanation

Because they run in opposite directions, their meeting points are determined by Alex's fraction of the total distance covered, which is 5 divided by 8. Their fourth meeting happens at 4 times 5 eighths, which equals 20 eighths, or 2 and 4 eighths of the track. The 4 eighths corresponds to half of the 800 m track, placing the fourth meeting point 400 m from the starting point.

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