Question

please answer, best answer will be brainlisted

Answer 1

Speed * Time= Distance    Let time taken for police to catch be n minutes

Total distance of the thief = 50(n+2)  As he has a head start of two mins

The Police goes in an AP [ 60,65,70...]    a= 60,  d= 5

Total distance covered=  n/2 [ 2a+(n-1)d]

Distance covered by police= distance covered by thief.

50 [n+2]  = n/2 [ 120 + 5n -5]

50[n+2] = n/2[ 115 +5n]

50[ n+2] = 5n/2 [ 23 + n]

10n +20 = n/2 [ 23+n]

20n +40 = 23n + n2

n2 + 3n -40= 0

n2 +8n -5n- 40 =0

n(n+8) - 5( n+8) =0

(n+8)(n-5)=  0          => n=-8 (or) n =5

n cannot be negative as it is the time taken. Hence n=5

The police will catch the thief after 5 minutes after the police starts to run or 7 mins after the theft happens as the police starts to run only after 2 mins.


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