A person can complete a journey in 22 hours. He covers the first one-third part of the journey at the rate of 15 km/h and the remaining distance at the rate of 45 km/h. What is the total distance of his journey (in km)?

Given:

Total time = 22 hours

First 1/3 distance speed = 15 km/h

Remaining 2/3 distance speed = 45 km/h

Formula used:

Time = Distance ÷ Speed

Let total distance = D km

Calculation:

⇒ Time for first 1/3 distance = (1/3)D ÷ 15 = D ÷ 45

⇒ Time for remaining 2/3 distance = (2/3)D ÷ 45 = 2D ÷ 135 = D ÷ 67.5

⇒ Total time = D ÷ 45 + D ÷ 67.5

Given: D ÷ 45 + D ÷ 67.5 = 22

⇒ LCM of 45 and 67.5 = 135

⇒ (3D + 2D) ÷ 135 = 22

⇒ 5D ÷ 135 = 22

⇒ D = (22 × 135) ÷ 5

⇒ D = 2970 ÷ 5 = 594 km

∴ Total distance is 594 km.