Shortcut Trick
Let the side of the square field be the LCM of given speeds, i.e., LCM(150, 300, 450, 600) = 1800 km.
Total Distance = 4 × 1800 = 7200 km.
Total Time = (1800 ÷ 150) + (1800 ÷ 300) + (1800 ÷ 450) + (1800 ÷ 600) = 12 + 6 + 4 + 3 = 25 hours.
Average Speed = Total Distance ÷ Total Time = 7200 ÷ 25 = 288 km/h.
∴ The correct answer is 288 km/h.
Alternate Method
150 km/h
300 km/h
450 km/h
600 km/h
Square Field
Side = d km
Given:
Speeds along the four sides of a square field are 150 km/h, 300 km/h, 450 km/h and 600 km/h.
Formula Used:
Average Speed = Total Distance ÷ Total Time
Time = Distance ÷ Speed
Calculations:
⇒ Let the distance of each side of the square be d km.
⇒ Total Distance around the field = d + d + d + d = 4d km.
⇒ Total Time taken = (d ÷ 150) + (d ÷ 300) + (d ÷ 450) + (d ÷ 600)
⇒ Taking LCM of 150, 300, 450 and 600, which is 1800.
⇒ Total Time = (12d + 6d + 4d + 3d) ÷ 1800
⇒ Total Time = 25d ÷ 1800 = d ÷ 72 hours.
⇒ Average Speed = 4d ÷ (d ÷ 72)
⇒ Average Speed = 4 × 72 = 288 km/h
∴ The correct answer is 288 km/h.
Additional Information
Average Speed for Two Equal Distances
When a person covers two equal distances at speeds x and y, the average speed is given by (2xy) ÷ (x + y).
Average Speed for Three Equal Distances
When a person covers three equal distances at speeds x, y and z, the average speed is given by (3xyz) ÷ (xy + yz + zx).
Average Speed for Unequal Distances
If distances d1, d2, d3... are covered at speeds v1, v2, v3... respectively, the average speed is (d1 + d2 + d3...) ÷ (t1 + t2 + t3...).