Question

A thief runs at a speed of 10m/s. A policeman runs behind him at a speed of 12.5m/s. But after 10 seconds the policeman had started running. After how many meters will the policeman catch the thief

Answer 1

Answer: 500m

Explanation:

The relative speed of policeman w.r.t thief is (12•5-10)m/s

=2•5m/s

As the policeman starts running after 10 sec, the dist. covered by thief in this period =v×t

=10×10

=100m

So rel. separation=100m

Time taken by policeman to catch thief = (rel. Separation)/(rel. vel.)

= 100/2•5

= 40sec

The dist covered by policeman in 40 sec = 40×12•5

= 500m

This is the answer.

Answer 2

Given : A thief runs at a speed of  10 mtr/ sec and a policeman runs at a speed of 12.5m/s but after 10 sec

To Find : after how many metes will the policeman catch the thief

Solution:

Distance = Speed x time

Let say Policeman  catches the thief after t sec

Speed of policeman  = 12.5 m/s

Distance covered by policemen  = 12.5t  m

Speed of Thief  = 10 m/s

Time for thief = t + 10 sec

Distance covered by policemen  = 10(t +10)  m

12.5t = 10(t + 10)

=> 2.5t  = 100

=> t  = 40

Distance covered by policemen  = 12.5t  

= 12.5 x 40

= 500 m

After running 500 m policeman catch the thief

Another Way : in 10 Sec  Thief covered Distance = 10 x 10 = 100 m

Relative Speed of Policeman = 12.5 - 10 =2.5 m/s

Time Taken by policeman = 100/2.5  = 40  sec

Distance covered by policemen  =  12.5 x 40=  500 m

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