Multiple choice

A cyclist leaves New York City at 8:00 AM and travels at a constant speed of 15 miles per hour towards Philadelphia. A car leaves New York City at 9:00 AM and travels at a constant speed of 60 miles per hour towards Philadelphia on the same route. At what time will the car overtake the cyclist?

  1. 9:15 AM

  2. 9:20 AM

  3. 9:45 AM

  4. 10:00 AM

  5. 10:15 AM
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The cyclist has a 1-hour head start, covering 15 miles. The relative speed of the car to the cyclist is 60 - 15 = 45 mph. To cover the 15-mile gap, the car needs 15/45 hours, which is 1/3 hour or 20 minutes; thus, it overtakes at 9:20 AM.

AI explanation

By 9:00 AM, the cyclist has traveled 15 miles, creating a 15-mile gap between them. The relative speed of the car compared to the cyclist is 60 minus 15, equaling 45 miles per hour. Using the formula time = distance divided by relative speed, the car catches up in 15 divided by 45 hours, which is one-third of an hour, or 20 minutes; therefore, the car overtakes the cyclist at 9:20 AM.

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