A person covers a distance on a scooter. If he had gone 3 km/h faster, he would have taken 40 minutes less; if he had gone 2 km/h slower, he would have taken 40 minutes more. What is the distance (in km)?

Introduction / Context:Two what-if changes to speed produce symmetric changes in time around the actual (unknown) scenario. Setting up time equations for the same distance at (v + 3), v, and (v − 2) allows solving for both v and distance D.

Given Data / Assumptions:

• Let actual speed = v km/h; distance = D km.
• D/(v + 3) = D/v − 2/3 h.
• D/(v − 2) = D/v + 2/3 h.

Concept / Approach:Use the pair of equations to eliminate D or v. Solving simultaneously yields concrete values that satisfy both constraints.

Step-by-Step Solution:

Verification / Alternative check:Both constraints are satisfied exactly for D = 40 km, confirming the solution.

Why Other Options Are Wrong:36, 37.5, 42.5, 45 km fail at least one of the two 40-minute differences.

Common Pitfalls:Assuming linearity in speed vs time change; not expressing both scenarios with the same D.

Final Answer:40