A thief commits a theft and runs at uniform speed of 50m/min. After 2 min a policeman runs at 60m in 1st min, increasing speed by tm/min. After how many min is the thief caught???
Answers
Answer:
Step-by-step explanation:
Speed of thief =50m/min
speed of policeman=60/min
Distance covered in 2m by thief=100m
relative speed=60-50 =10m/min
Time=Distance/speed
Time=100/10
Time=10min
Ans=10min
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