# Circular Tracks Difficult-YouTube Lecture Handouts

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• Circumference of 90 centimeters is divided into three equal lengths. Ants A, B, and C start to crawl clockwise starting from one of the three points. A is ahead of B and B is ahead of C at speeds 3 cm/s, 5 cm/s, & 10 cm/s. How long does it take for the three ants to arrive at the same spot for the first time?

• Amy and Amanda walk on a circular track. Amy starts from spot A, and Amanda starts from spot B. They walk in opposite directions. After 6 minutes, they meet, 4 more minutes later, Amy arrives at spot B. 8 more minutes later, they meet again. How many minutes does it take for both to walk the full circle?

• A and B start running in opposite directions (towards each other) on a circular track starting at diametrically opposite points. They first meet after A has run for 75m and then they next meet after B has run 100 m after their first meeting. Find circumference of the track.

• Two friends A and B simultaneously start running around a circular track. They run in the same direction. A travels at 6 m/s and B runs at b m/s. If they cross each other at exactly two points on the circular track and b is a natural number less than 30, how many values can b take?

• Three friends A, B and C decide to run around a circular track. They start at the same time and run in the same direction. A is the quickest and when A finishes a lap, it is seen that C is as much behind B as B is behind A. When A completes 3 laps, C is the exact same position on the circular track as B was when A finished 1 lap. Find the ratio of the speeds of A, B and C?