A woman covers a certain distance on scooty. Had she moved 3 km/hr faster, she…

2025

A woman covers a certain distance on scooty. Had she moved 3 km/hr faster, she would have taken 45 minutes less. If she had moved 2 km/hr slower, she would have taken 45 minutes more. The distance (in km) is

  1. A.

    42.5

  2. B.

    40

  3. C.

    37.5

  4. D.

    45

Attempted by 2 students.

Show answer & explanation

Correct answer: D

Step-by-Step Solution

To solve this problem, we use the formula: Distance = (Speed1 * Speed2 / Difference in Speeds) * Difference in Time.

  1. Define variables:

    • Let distance be d and usual speed be s.

    • Time difference of 45 minutes = 0.75 hours.

  2. Set up equations for the two scenarios:

    • Case 1 (3 km/hr faster): d = (s * (s + 3) / 3) * 0.75

    • Case 2 (2 km/hr slower): d = (s * (s - 2) / 2) * 0.75

  3. Equate and solve for speed (s):

    • Since distance d is the same: (s * (s + 3) / 3) * 0.75 = (s * (s - 2) / 2) * 0.75

    • (s + 3) / 3 = (s - 2) / 2

    • 2s + 6 = 3s - 6

    • s = 12 km/hr.

  4. Calculate the distance (d):

    • Substitute s = 12 into Case 1: d = (12 * (12 + 3) / 3) * 0.75

    • d = (12 * 15 / 3) * 0.75

    • d = 60 * 0.75 = 45 km.

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