Multiple choice

John and Sarah are riding their bikes in a clockwise direction around a circular track that is 600 meters in circumference. They maintain a constant speed, with John covering a distance of 1,200 meters every eight minutes and Sarah covering the same distance every ten minutes. If John and Sarah commence their cycling from opposite points on the circular track, how long will it take for John to cycle and catch up with Sarah second time?

  1. 20 minutes

  2. 30 minutes

  3. 35 minutes

  4. 45 minutes

  5. 48 minutes
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

John speed = 1200/8 = 150 m/min. Sarah speed = 1200/10 = 120 m/min. Relative speed = 150 - 120 = 30 m/min. They start at opposite points (300m apart). To catch up the first time, John must cover the 300m gap. Time = 300 / 30 = 10 min. To catch up the second time, he must cover another 600m (the full track). Time = 600 / 30 = 20 min. Total time = 10 + 20 = 30 min.

AI explanation

Using the formula Speed equals Distance divided by Time, John's speed is 1200 divided by 8, giving 150 meters per minute, and Sarah's speed is 1200 divided by 10, giving 120 meters per minute. The relative speed is 150 minus 120, which equals 30 meters per minute. Because they start at opposite points on the 600 meter track, the initial distance between them is 300 meters, and for John to catch up with Sarah the second time, he must cover this initial gap plus one full lap, meaning a total relative distance of 900 meters. The time taken is Relative Distance divided by Relative Speed, which is 900 divided by 30, equaling 30 minutes. The result is 30.

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