Two cyclists start from the same point at the same time: one north at 18 km/h and the other south at 20 km/h. After how long will they be 95 km apart?
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A4 h 30 min
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B4 h 45 min
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C5 h 16 min
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D2 h 30 min
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ENone of these
Answer
Correct Answer: 2 h 30 min
Explanation
Introduction / Context:When two objects move in opposite directions along a straight line, their separation grows at the sum of their speeds. This yields time directly from distance = rate * time.
Given Data / Assumptions:
- Cyclist A speed = 18 km/h (north).
- Cyclist B speed = 20 km/h (south).
- Desired separation = 95 km.
Concept / Approach:Relative separation speed = 18 + 20 = 38 km/h. Then time t = distance / rate.
Step-by-Step Solution:t = 95 / 38 h = 2.5 h.Convert 0.5 h = 30 min → t = 2 h 30 min.
Verification / Alternative check:In 2.5 h, A covers 45 km and B covers 50 km, totaling 95 km separation.
Why Other Options Are Wrong:Other times correspond to separations different from 95 km when multiplied by 38 km/h.
Common Pitfalls:Subtracting speeds (used for same-direction chasing) instead of adding for opposite directions.
Final Answer:2 h 30 min