While going to a shopping mall, Nishi travels at a speed of 68 km/hr and on…

CONCEPT: When a traveller covers the SAME one-way distance at two different speeds (going and returning), the average speed for the whole round trip is NOT the plain arithmetic mean of the two speeds. Because time = distance / speed, the time spent on each leg differs even though the distance is equal, so the correct measure is the harmonic mean of the two speeds: Average speed = (2 v1 v2) / (v1 + v2).

1. Identify the two speeds for the equal one-way distances: v1 = 68 km/hr for the onward trip to the mall, and v2 = 92 km/hr for the return trip.

2. Add the two speeds: v1 + v2 = 68 + 92 = 160.

3. Multiply the two speeds: v1 × v2 = 68 × 92 = 6256.

4. Double the product: 2 × 6256 = 12512.

5. Divide the doubled product by the sum of the speeds: 12512 ÷ 160 = 78.2 km/hr.

CROSS-CHECK: let the one-way distance be d km. Time for the onward trip = d/68 hr and time for the return trip = d/92 hr, so total time = d(92 + 68) / (68 × 92) = 160d / 6256 hr, covering a total distance of 2d km. Average speed = 2d ÷ (160d / 6256) = 2 × 6256 / 160 = 78.2 km/hr, which matches the value found above.