Manthan took part in a marathon in which he cycled some distance at 20 km/hr and ran some distance at 12 km\hr. If he completed the marathon of 151 km in 9 hours and 45 minutes, then find for how much time Manthan ran during the marathon. 

Manthan took part in a marathon in which he cycled some distance at 20 km/hr and ran some distance at 12 km\hr. If he completed the marathon of 151 km in 9 hours and 45 minutes, then find for how much time Manthan ran during the marathon.  Correct Answer 5 hrs 30 min

Given:

Cycling speed during marathon = 20 km/hr

Running speed during marathon = 12 km/hr

The total distance of Marathon = 151 km

Total time taken to complete the marathon = 9 hrs 45 min = 9 hrs + 3/4 hrs = 9.75 hrs

Concept Used:

Average Speed = (Total distance)/(Total Time)

Calculation:

Let the time for which Manthan ran during the marathon be x hrs.

So, the time for which Manthan cycled during the marathon = (9.75 - x) hrs

According to the question,

Average Speed = (Total distance)/(Total Time)

⇒ 151/9.75 = {Distance travelled by running + Distance travelled by cycling)/Total time

⇒ 151/9.75 = {12 × x + 20 × (9.75 - x)}/9.75

⇒ 151 = 12x + 195 - 20x

⇒ 20x - 12x = 195 - 151

⇒ 8x = 44

⇒ x = 44/8

⇒ x = 5.5 hrs

⇒ x = 5 hrs + 0.5 hrs

⇒ x = 5 hrs 30 min

∴ Manthan ran for a duration of 5 hrs 30 min during the marathon.