Two railway units separated by 120 miles proceed toward each other at 70 mph (1st unit) and 50 mph (2nd unit). Concurrently, an avian creature departs from the faster unit toward the slower one at 85 mph, immediately reversing direction upon reaching the slower unit, maintaining identical speed. Upon reaching the faster unit again, it reverses and repeats this cycle continuously. When the trains collide, what total distance has the avian traveled?
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Answer: A. 85 miles
Explanation
The closing speed between the two approaching railway units is the sum of their individual speeds, seventy plus fifty. Dividing the initial separation distance of one hundred twenty miles by the closing speed of one hundred twenty miles per hour gives one hour. The avian creature flies continuously at eighty five miles per hour for that exact duration of one hour, covering eighty five miles. Relative speed when two objects move toward each other is calculated by adding their individual motion velocities together. Total travel distance equals the constant speed of the moving object multiplied by the total elapsed travel time. Continuous motion problems can often be solved simply by finding the total elapsed time until an interception event occurs.
Seventy miles corresponds to the speed of the first railway unit rather than the total distance flown by the avian. Fifty miles corresponds to the speed of the second railway unit rather than the calculated avian travel distance. One hundred twenty miles equals the initial separation distance between the trains rather than the distance flown.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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