Hello, MathLearner!

Aruneem travels from Patna to Calcutta, a distance of 200 km at the speed of 40 km/hr.

At the same time, Nilanjan starts from Calcutta at a speed of 20 km/hr along a road

which is perpendicular to the road on which Aruneem is travelling.

When will Aruneem and Nilanjan be closest to each other?

Answer: in 4 hours Code:

40t A 200-40t
P * - - - - - * - - - - - - - - * C
* |
* |
* | 20t
* |
* |
* B

Aruneem starts at and travels toward at 40 km/hr.

. . After hours, he has travelled km to point

Note that: .

At the same time, Nilanjan starts at and travels south at 20 km/hr.

. . After hours, he has travelled km to point

Their distance is , the hypotenuse of right triangle

Hence: .

Then: .

Therefore, minimum distance occurs in 4 hours.