Walk one way, drive back — total 6 h 45 min; driving both saves 2 h: Amit walks from A to B and returns by car; total time = 6 h 45 min. If he had driven both ways, the total would be 2 h less. How long would walking both ways take?

Difficulty: Medium

Correct Answer: 8 h 45 min

Explanation:

Introduction / Context:This is the same structure as mixed-mode round trips. Express the knowns in terms of one-way walking and driving times and use the given saving to find the all-walking time.

Given Data / Assumptions:

  • t_walk_one_way + t_drive_one_way = 6.75 h
  • Driving both ways = 2 * t_drive_one_way = 6.75 − 2 = 4.75 h

Concept / Approach:Find t_drive_one_way, then t_walk_one_way, and finally double the walking time for both ways.

Step-by-Step Solution:

2 * t_drive_one_way = 4.75 ⇒ t_drive_one_way = 2.375 ht_walk_one_way = 6.75 − 2.375 = 4.375 hWalking both ways = 2 * 4.375 = 8.75 h = 8 h 45 min

Verification / Alternative check:Check saving: (t_walk + t_drive) − (2 * t_drive) = t_walk − t_drive = 2 h.

Why Other Options Are Wrong:They conflict with the given totals.

Common Pitfalls:Forgetting that “2 h less” applies to the total round-trip time.

Final Answer:8 h 45 min

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