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 $60m$ in first minute and increases his speed by $5$m/minute every succeeding minute. After how many minutes, the poilceman will catch the thief?

Answer 1

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
$t/2(2\times 60+(t-1)\times 5)=50t+100$
$t\times (120+5t-5)=100t+200$
$5t^2+15t-200=0$
$t^2+3t-40=0$
$t=\{-3\pm \sqrt{(9+160)\}/2}=(-3\pm 13)/2=+5$
Implies, police will catch thief in 5 minutes.