A man travels for 35 km at two constant speeds: 4 km/h for some time and 5 km/h for the rest. If, instead, he had swapped the speeds for those same time portions, he would cover 2 km more in the same total time. What is the total time at the original plan?

Introduction / Context:
The statement implies fixed time portions at two speeds. Swapping the speeds across the same time portions changes total distance while total time remains unchanged. This yields two linear equations in the two time portions whose sum is the desired total time.

Given Data / Assumptions:

• Original distance = 35 km at speeds 4 km/h and 5 km/h over time portions t1 and t2.
• Swapped speeds for the same times produce distance 37 km (2 km more) in the same total time.
• No stoppages; uniform speeds.

Concept / Approach:
Original distance: 4t1 + 5t2 = 35. Swapped distance: 5t1 + 4t2 = 37. Add equations to eliminate alternately and obtain t1 + t2 (the total time).

Step-by-Step Solution:
(4t1 + 5t2) + (5t1 + 4t2) = 35 + 37 → 9(t1 + t2) = 72.Total time T = t1 + t2 = 72/9 = 8 hours.

Verification / Alternative check:
Subtract equations: (5t1 + 4t2) − (4t1 + 5t2) = 37 − 35 → t1 − t2 = 2. With T = 8, solve t1 = 5, t2 = 3; original distance = 4*5 + 5*3 = 35; swapped = 5*5 + 4*3 = 37, as stated.

Why Other Options Are Wrong:
7, 9, or 4.5 hours do not satisfy both distance equations simultaneously.

Common Pitfalls:
Interpreting the statement as swapping distances rather than speeds for the same times; failing to note total time remains fixed.

Final Answer:
8 hours