Problem:A circular track has a circumference of 2𝜋2π miles. Runner A can complete one lap in 20 minutes, while Runner B can complete one lap in 30 minutes. If both runners start at the same point and run in the same direction, how long will it take for Runner A to overtake Runner B?
Question
Problem:A circular track has a circumference of 2𝜋2π miles. Runner A can complete one lap in 20 minutes, while Runner B can complete one lap in 30 minutes. If both runners start at the same point and run in the same direction, how long will it take for Runner A to overtake Runner B?
Solution
Step 1: Understand the problem The problem is asking for the time it will take for Runner A to overtake Runner B on a circular track.
Step 2: Determine the speed of each runner The speed of a runner is calculated by dividing the distance (in this case, the circumference of the track) by the time it takes to cover that distance.
For Runner A, the speed is 2π miles per 20 minutes = π/10 miles per minute. For Runner B, the speed is 2π miles per 30 minutes = π/15 miles per minute.
Step 3: Determine the relative speed When two objects are moving in the same direction, the relative speed is the difference of their speeds. So, the relative speed of Runner A with respect to Runner B is (π/10 - π/15) miles per minute = π/30 miles per minute.
Step 4: Calculate the time it takes for Runner A to overtake Runner B The time it takes for Runner A to overtake Runner B is the distance of the track divided by the relative speed. So, the time is 2π miles / (π/30 miles per minute) = 60 minutes.
So, it will take 60 minutes for Runner A to overtake Runner B.
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