Shortcut Trick
Let the Total Distance be 100 km.
Time taken for first part = 30 ÷ 90 = 1/3 hour.
Time taken for second part = 45 ÷ 135 = 1/3 hour.
Time taken for remaining part (25%) = 25 ÷ 75 = 1/3 hour.
Total Time = 1/3 + 1/3 + 1/3 = 1 hour.
Average Speed = 100 km ÷ 1 hr = 100 km/h.
∴ The correct answer is 100 km/h.
Alternate Method
Given:
Distance1 = 30%, Speed1 = 90 km/h
Distance2 = 45%, Speed2 = 135 km/h
Distance3 = 100% − (30% + 45%) = 25%, Speed3 = 75 km/h
Formula Used:
Average Speed = Total Distance ÷ Total Time
Time = Distance ÷ Speed
Calculations:
Let total distance be D.
⇒ Total Time (T) = (0.3D ÷ 90) + (0.45D ÷ 135) + (0.25D ÷ 75)
⇒ T = (D ÷ 300) + (D ÷ 300) + (D ÷ 300)
⇒ T = 3D ÷ 300
⇒ T = D ÷ 100
⇒ Average Speed = D ÷ (D ÷ 100)
⇒ Average Speed = (D × 100) ÷ D
⇒ Average Speed = 100 km/h
∴ The correct answer is 100 km/h.
Additional Information
Average Speed for Equal Distances
If a journey is divided into 'n' equal distances with speeds v1, v2, ..., vn, then Average Speed is the Harmonic Mean of the speeds.
Average Speed for Two Equal Halves
When two equal distances are covered at speeds 'a' and 'b', Average Speed = (2 × a × b) ÷ (a + b).
Unit Conversion
To convert speed from km/h to m/s, multiply by 5/18. To convert from m/s to km/h, multiply by 18/5.