Round trip with mode switch — time saved by cycling both ways: Going on foot one way and by cycle the other takes 5 h 45 min total. Cycling both ways would save 2 h. What is the time to walk both ways?
Aptitude
Time and Distance
Difficulty: Medium
Choose an option
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A6 h 45 min
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B7 h 45 min
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C8 h 15 min
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D8 h 30 min
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E7 h 15 min
Answer
Correct Answer: 7 h 45 min
Explanation
Introduction / Context:Let the one-way walking time and cycling time be variables. Use the total-time condition and the “save 2 h if cycle both ways” condition to solve for the walking-only round-trip time.
Given Data / Assumptions:
- Current total: t_walk + t_cycle = 5.75 h
- Cycling both ways total: 2 * t_cycle = 3.75 h
Concept / Approach:Solve for t_cycle, then t_walk, then double t_walk for walking both ways.
Step-by-Step Solution:
2 * t_cycle = 3.75 ⇒ t_cycle = 1.875 ht_walk = 5.75 − 1.875 = 3.875 hWalking both ways = 2 * 3.875 = 7.75 h = 7 h 45 minVerification / Alternative check:Check difference: (t_walk + t_cycle) − (2 * t_cycle) = t_walk − t_cycle = 2 h.
Why Other Options Are Wrong:Other totals contradict either the given 5 h 45 min or the 2 h saving.
Common Pitfalls:Converting minutes to hours incorrectly or mixing single-way vs round-trip quantities.
Final Answer:7 h 45 min