Shortcut Trick
For three equal distances, Average Speed = 3 × s1 × s2 × s3 ÷ (s1s2 + s2s3 + s3s1)
Average Speed = 3 × 5 × 10 × 15 ÷ (50 + 150 + 75)
Average Speed = 2250 ÷ 275 = 90 ÷ 11
Average Speed = 8(2/11) km/h
∴ The correct answer is 8(2/11) km/h.
Alternate Method
Given:
Speeds for three equal parts: s1 = 5 km/h, s2 = 10 km/h, s3 = 15 km/h.
Formula Used:
Average Speed = Total Distance ÷ Total Time
Calculations:
⇒ Let each equal part of the distance be the LCM of 5, 10, and 15, which is 30 km.
⇒ Total Distance = 30 + 30 + 30 = 90 km
⇒ Time taken for 1st part (t1) = 30 ÷ 5 = 6 hours
⇒ Time taken for 2nd part (t2) = 30 ÷ 10 = 3 hours
⇒ Time taken for 3rd part (t3) = 30 ÷ 15 = 2 hours
⇒ Total Time = 6 + 3 + 2 = 11 hours
⇒ Average Speed = 90 ÷ 11 = 8(2/11) km/h
∴ The correct answer is 8(2/11) km/h.
Additional Information
Average Speed for Two Equal Distances
When a journey is divided into two equal distance parts with speeds x and y, Average Speed = 2xy ÷ (x + y).
Average Speed for Equal Time Intervals
If a person travels at different speeds for equal time intervals, Average Speed is the simple arithmetic mean: (v1 + v2 + ... + vn) ÷ n.
Relative Speed
For objects moving in the same direction, relative speed = |s1 − s2|. For opposite directions, relative speed = s1 + s2.