
Shortcut Trick
Average speed is the weighted average of given speeds using time as weights.
Ratio of time intervals = 10 minutes : 15 minutes = 2 : 3
Average Speed = (S1 × T1 + S2 × T2) ÷ (T1 + T2)
Average Speed = (48 × 2 + 60 × 3) ÷ (2 + 3)
Average Speed = (96 + 180) ÷ 5 = 276 ÷ 5 = 55 1/5 km/h
∴ The correct answer is 55 1/5 km/h.

Alternate Method
Given:
Speed S1 = 48 km/h, Time T1 = 10 minutes = 10/60 = 1/6 hours
Speed S2 = 60 km/h, Time T2 = 15 minutes = 15/60 = 1/4 hours
Formula Used:
Distance = Speed × Time
Average Speed = Total Distance ÷ Total Time
8 km
48 km/h, 10 min
15 km
60 km/h, 15 min
Total Distance = 23 km | Total Time = 25 min
Average Speed = 55 1/5 km/h
Calculations:
⇒ D1 = 48 × (1/6) = 8 km
⇒ D2 = 60 × (1/4) = 15 km
⇒ Total Distance = 8 + 15 = 23 km
⇒ Total Time = 10 + 15 = 25 minutes = 25/60 = 5/12 hours
⇒ Average Speed = 23 ÷ (5/12) = (23 × 12) ÷ 5
⇒ Average Speed = 276 ÷ 5 = 55 1/5 km/h
∴ The correct answer is 55 1/5 km/h.

Additional Information
Average Speed (Different Distances & Times)
Average Speed is always defined as Total Distance ÷ Total Time. It is not the simple average of individual speeds unless the time intervals are strictly equal.
Average Speed (Equal Distances)
If a person covers two equal halves of a journey at speeds x and y, the Average Speed = 2xy ÷ (x + y).
Average Speed (Equal Time Intervals)
If a person travels at speeds x and y for equal amounts of time, the Average Speed simplifies to (x + y) ÷ 2.