a thief runs with a uniform speed of 100m/minute . after one minute, a police man run after the thief to catch him. he goes with the seed of 100m/minutes in the first minute and increase speed by 10m/minute every succeeding meter. after hom many minutes the police man will catch the thief?
Answers
Answer:
Let the police catch the thief in n min
As the thief ran 1 min before the police...time taken by the thief before being caught = (n+1) min
Distance travelled by the thief in (n+1) min = 100(n+1)m
Speed of police in 1st min=100m/min
Speed of police in 2nd min=110m/min
...3rd min = 120m/min.........so on
100,110,120,............ this forms an AP
Total distance travelled by the police in n min = n/2(2 x 100 +(n-1)10)
On catching the thief by police,distance traveled by thief= distance travelled by the police
100(n+1)= n/2(2 x 100 + (n-1)10)
100n + 100= 100n +n/2(n-1)10
100=n(n-1)5
n2 -n-20 = 0
(n-5)(n+4) = 0
n-5 = 0
n= 5 OR n= -4...(but this is not possible)
so, n= 5
Time taken by the policeman to catch the thief = 5min
Answer:
AFTER TWELVE MINUTES TH POLICE WILL CATCH THE THEIF
Step-by-step explanation:
after a minute when police starts to run the distance between police and thief is 100m
police covers 100m in second min but theif cover 200m
in third min police covers 210m but theif cover 300m
in fourth min police covers 320m but theif covers 400
in fifth min police covers 430m but theif covers 500 m
in sixth min police covers 540m but theif covers 600m
in seventh min police covers 650m but theif covers 700m
in eighth min police covers 760m but thief covers 800m
in ninth min police covers 870m but thief covers 900m
in tenth min police covers 980m but thief covers 1000m
in eleventh min police covers 1090m but thief covers 1100m
in twelveth min police covers 1200m but thief covers 1200m