Question

a thief runs from a police station at a uniform speed of 100m per.after 1 minute a policeman runs behind the thief to catch him.he goes at a speed of 8m/minute in the first minute and increases his speed by 10m/minute in each succeeding minute.after how many minutes will the policeman catch the thief

Answer 1

the policeman will get the theif in 21 minutes.
you have to increase the speed of the policeman by 10m/min every minute.
i made a table that conists of one column for time and the other two for policeman and the theif.As the speed of the policeman increased,he was able to catch the theif when his speed was 208m/min.
hope it helps. :)

Answer 2

Step-by-step explanation:

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here....

theif's speed=100m./min

let time taken by police before catch the thief =x

then the time of theif being catched=x+1

as the police increase his speed=10m./min every minute

his time taken as AP-100,110,120....

Distance of the thief = $time ×speed \\</p><p> =100×(x+1)\\</p><p> =100x+100..........(1)$

Distance covered by police =sum of x terms of AP

=Sn=x/2(2×100+(x-1)10)

=Sn=x(100+5x-5)

=Sn=95x-5x^2...........(2)

as the distance covered by police and theif are same...

=equation 1=equation 2

= 95x-5x^2=100x+100

=5x^2-5x-100=0

= x^2-x-20=0

we solve the equation and get...

x=-4 and x=5

[as the time can't be negative]

= X=5

the time taken by police to catch the thief = 5 minutes