Question

A man divides his journey into 3 parts of 48 km, 25km, and D km, he travels with a speed of 8 km/h, 5 km/h and 6 km/h respectively for these distances. Find the value of 'D'  in km, if the average speed for the whole journey is 6.5 km/h.   
1. 10
2. 15
3. 18
4. 20 

Answer 1

Correct Answer - Option 3 : 18

Given :

A man divides his journey into 3 parts of 48 km, 25km, and D km. 

He travels with a speed of 8 km/h, 5 km/h and 6 km/h respectively for these distances.

Formula used :

Average speed = Total distance/Total time taken 

Calculations :

Total distance for the whole journey = 48 + 25 + D = 73 + D 

Total time for whole journey = (48/8) + (25/5) + (D/6)    (time = distance/speed)

⇒ 11 + (D/6) 

Now, 

Average speed =  (73 + D)/[11 + (D/6) 

6.5 = (73 + D)/[11 + (D/6) 

13/2 = (73 + D)/[11 + (D/6) 

⇒ D/6 = 3 

⇒ D = 18 km 

∴ The value of D is 18 km