A thief was spotted by a policeman at a distance of 1200m and he started chasing him. The thief ran 6.4km in 52 minutes and the policeman also ran the same distance in 40 minutes. Find the distance the thief had run before he was caught.

First, let us determine the speeds of both the thief and the policeman.
Speed of Thief (V
t
​
):

V
t
​
=
52min
6.4km
​
=
52×60s
6400m
​
=
39
80
​
m/s
Speed of Policeman (V
p
​
):

V
p
​
=
40min
6.4km
​
=
40×60s
6400m
​
=
3
8
​
m/s=
39
104
​
m/s
Relative speed (V
p
​
−V
t
​
):

V
rel
​
=
39
104
​
−
39
80
​
=
39
24
​
m/s
Time taken to catch the thief (t):

t=
V
rel
​

Initial Distance
​
=
39
24
​

1200
​
=
24
1200×39
​
=50×39=1950seconds
Distance run by the thief in this time:

D=V
t
​
×t=
39
80
​
×1950=80×50=4000m=4km