Half of the total journey is covered at the speed of 90 km/hr, while 1/3 of total journey is covered at the speed of 75 km/hr and 1/6 of total journey is covered at the rate of 50 km/hr. Find the average speed of the whole journey in m/s if distance of total journey is 900 km.?

Option 5 : 125/6 m/s

Given:

Total journey = 900 km

Half of total journey is covered at the speed of 90 km/hr

1/3 of total journey is covered at the rate of 75 km/hr

1/6 of total journey is covered at the rate of 50 km/hr

Concept used:

Average speed = Total Distance/Total time taken

Speed in m/s = speed in km/hr × 5/18

Calculation:

Total journey = 900 km

Half of the total journey = 450 km

⇒ 450 km is covered at the rate of 90 km/hr

⇒ Time taken to cover 450 km = 450/90 = 5 hours

Now, 1/3 of total journey = 300 km

⇒ 300 km is covered at the rate of 75 km/hr

⇒ Time taken to cover 300 km = 300/75 = 4 hours

Now, 1/6 of the total journey = 150 km

⇒ 150 km is covered at the rate of 50 km/hr

⇒ Time taken to cover 150 km = 3 hours

Now, Total time taken to cover whole journey = (5 + 4 + 3) hours

⇒ Total time taken = 12 hours

Average speed of the whole journey = 900/12

⇒ Average speed of the whole journey = 75 km/hr

 Speed in m/s = speed in km/hr × 5/18

⇒ As we know, Speed in m/s = speed in km/hr × 5/18

⇒ Speed in m/s = 75 × 5/18