Person A starts walking from a point towards a place 7 miles away at a speed of 1 mile in 8 minutes. Person B starts from the same point 4 minutes after A. When A reaches the destination, turns back and walks 1 mile, he meets B. If A's speed is 1 mi…

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Introduction / Context: This question combines time, distance and relative motion for walkers starting at different times. Instead of asking for speed directly in km/h or miles per hour, it asks for how many minutes B takes per mile, which is a slightly different but equivalent measure of speed. Given Data / Assumptions: Distance from starting point to destination = 7 miles. Person A speed = 1 mile in 8 minutes. Person B starts 4 minutes after A from the same point. A reaches the destination, turns back, walks 1 mile back and meets B at that point. We assume straight path and constant speeds for both persons. Concept / Approach: Compute the total time A has been walking before meeting B. Use that to find how long B has been walking. Since we know B covers 6 miles (from start to meeting point 1 mile short of destination), we can determine how many minutes B takes per mile by dividing his walking time by his distance. Step-by-Step Solution: A walks from start to destination: 7 miles. Time for A to reach destination = 7 * 8 = 56 minutes. A then walks 1 mile back: extra 8 minutes. Total walking time for A before meeting B = 56 + 8 = 64 minutes. B starts 4 minutes after A, so B has been walking for 64 - 4 = 60 minutes by the meeting time. Meeting point is 1 mile from destination, so it is 7 - 1 = 6 miles from start. Therefore B walks 6 miles in 60 minutes. Minutes per mile for B = 60 / 6 = 10 minutes per mile. Verification / Alternative check: B's speed in miles per hour = 60 minutes / 10 minutes per mile = 6 miles per hour. In 1 hour B travels 6 miles; in 60 minutes in the scenario he also travels 6 miles, which is consistent. Why Other Options Are Wrong: 9 minutes per mile would mean 6.67 miles in 60 minutes, so B would be closer to or past the destination, which contradicts the meeting point. 12 minutes per mile gives only 5 miles in 60 minutes, so B would not have reached the meeting point that is 6 miles away. 8 minutes per mile implies B walks as fast as A, in which case their meeting pattern and start time difference would not match the given situation. Common Pitfalls: Some learners forget to include the time A spends walking back 1 mile, thinking they meet exactly at the destination. Another mistake is to assume 7 miles is the distance B walks and then divide the time incorrectly. Always clearly mark distances on a mental or rough diagram and carefully account for each phase of the motion. Final Answer: B's speed is such that he takes 10 minutes per mile.

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