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)?

Difficulty: Medium

42.5
36
37.5
40
45

Correct Answer: 40

Explanation:

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:

From the system, the consistent solution is v = 12 km/h and D = 40 km.Check faster case: time at 12 vs 15 km/h differs by (D/12 − D/15) = 40(1/12 − 1/15) = 40(1/60) = 2/3 h = 40 min.Check slower case: time at 10 vs 12 km/h differs by 40(1/10 − 1/12) = 40(1/60) = 2/3 h = 40 min.

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.

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)?

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