Question

A thief, after committing a theft runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every suceeding minute. After how many minutes, the policeman will catch the theif?​

Answer 1

The police will catch the thief in 5 minutes.

Explanation:

Distance between thief and police after 2 minutes = 100 m

Implies, thief covers total 100 + 50t m

The police runs with the following patterns 60,65,70...

This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t

t/2 (2 × 60+ (t − 1) ×5)= 50t + 100

t× (120 + 5t −5)= 100t + 200

​(−3+13)÷2= 5

So, the police will catch the thief in 5 minutes.