A runs 1 2/3 times faster than B. Giving B an 80 m head start, how far should the finish line be so both arrive simultaneously?
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Answer: A. 200 m
Explanation
Runner A covers distance faster, allowing them to overcome the initial head start. The speed ratio indicates A covers five units of distance for every three of B. Equating the time taken for both runners to reach the finish yields 200 meters. A speed is expressed as 5/3 times the running speed of competitor B. Head start distance given to runner B equals exactly 80 meters at the start. Simultaneous arrival means both runners spend the exact same amount of running time.
Handicapped races in sports provide practical examples of relative speed and distance calculations. Logistics planning frequently involves intercept calculations similar to pursuit problems. Understanding proportional speeds helps in analyzing mechanical and kinetic systems. Choosing 300 meters fails to satisfy the proportional time equality for both runners. Choosing 270 meters miscalculates the distance required to neutralize the head start. Choosing 160 meters underestimates the necessary track length for simultaneous arrival.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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