A person has to reach a certain place at a certain time and he finds that he will be 15 minutes late if he walks at 4 km/hr and 10 minute earlier, if he walks at 6km/hr. Find the distance he has to cover?

Concept Used:-

The time required to cover a distance by an object is equal to the ratio of distance to the speed of the object.

⇒ Time = Distance / Speed

Explanation:-

Suppose that the distance which person need to cover is X km.

Time required to cover this distance with 4 km/hr,

⇒ T₁ = X / 4

Time required to cover this distance with 6 km/hr,

⇒ T2 = X / 6

Now according to the question, the difference between these time is the addition of 15 minutes and 10 minutes. Thus,

⇒ T1 - T2 = (15 / 60) + (10 / 60)

⇒ (X / 4) - (X / 6)= (15 / 60) + (10 / 60)

⇒ (3X + 2X) / 12 = (15 + 10 ) / 60

⇒ X / 12 = 25 / 60

⇒ X / 12 = 5 / 12

⇒ X = 5 km

So, the distance which person need to cover is 5 km.

Hence, the correct option is 3.