Question

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

Answer 1

theft cover 100 m in 2 min
then police start after 1 min he cover's 60m


theft in 7min 350m
police 5 min 350m
police catch the theft in 5 min

Answer 2

Answer:

According to the question,

Distance between thief and police after 2 minutes = 100 m

Police starts chasing thief with initial speed of 60 and increasing his speed by 5 m every minute.

Let the police chase the thief for t minutes.

Implies, thief covers total 100 + 50t m

Police runs with following pattern 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

5t

2

+15t−200=0

t

2

+3t−40=0

t={−3±

(9+160)}/2

=(−3±13)/2=+5

Implies, police will catch thief in 5 minutes

or the thief will be caught in 7 minutes