Time and Distance – Compare walking and driving times: A person can go one way by walking and return by driving in a total of 6 hours. Walking both ways would take 10 hours. How long would it take if the person drives both ways?

Introduction / Context:Let the one-way distance be D, walking speed be w, and driving speed be v. Translate each scenario into time equations and solve for the unknown driving-only round-trip time 2D/v.

Given Data / Assumptions:

• D/w + D/v = 6 h for walk one way and drive back.
• 2D/w = 10 h for walking both ways.
• All speeds are constant.

Concept / Approach:From 2D/w = 10, we get D/w = 5. Substitute into the mixed trip to find D/v, which then yields the driving-only round-trip time 2D/v.

Step-by-Step Solution:D/w = 5 ⇒ D/v = 6 − 5 = 1.Hence 2D/v = 2 * 1 = 2 h.

Verification / Alternative check:Interpretation: One-way drive time is 1 h; round-trip drive is 2 h. With D/w = 5 h, the mixed trip is 5 + 1 = 6 h, consistent.

Why Other Options Are Wrong:Any value other than 2 h fails to satisfy both original equations simultaneously.

Common Pitfalls:Solving for speeds rather than times or misinterpreting which equation corresponds to which scenario.

Final Answer:2 h