Plz answer this.............!
Answers
Answer:
5 min
Step-by-step explanation:
Let the policeman catch the thief in n minutes.
Given that uniform speed of the thief = 100m/min.
Given that After 1 minute a policeman runs to catch him at the speed of 100 in first minutes.
(n + 1) minutes = 100(n + 1) minutes.
Given that speed of policeman increase by 10m/min.
The speed of police in 1 minute = 100m/min.
The speed of police in 2 minutes = 110m/min.
The speed of police in 3 minutes = 120m/min.
The speed of police in 4 minutes = 130m/min.
Hence 100,110,120,130 are in AP.
Let a be the first term and d be the common difference.
a = 100,d = 110 - 100 = 10.
We know that sum of n terms of an ap = n/2(2a + (n - 1) * d)
= n/2(2(100) + (n - 1) * 10) ------ (1)
The distance traveled by the thief = Distance traveled by the police
100(n + 1) = n/2(2 * 100+ (n - 1) * 10)
100n + 100 = n/2(200 + 10n - 10)
200n + 200 = 10n^2 + 190n
10n^2 + 190n - 200 = 200n
10n^2 - 10n - 200 = 0
n^2 - n - 20 = 0
n^2 -5n + 4n - 20 = 0
n(n - 5) + 4(n - 5) = 0
(n -5)(n + 4) = 0
n = 5 (or) n = -4.
n cannot be negative.
Therefore the time is taken by the policeman to catch the thief = 5minutes.