A policeman spots a thief from a distance of 100 metres. When he starts running after the thief, the thief starts running as well. How far will the thief have to run before being overtaken if his speed is 8 km/h and the policeman's speed is 10 km/h?

Given:
Distance between policeman and thief = 100m=0.1km
Speed of thief (v
t
​
) = 8km/h
Speed of policeman (v
p
​
) = 10km/h

Relative speed of policeman with respect to thief:

v
rel
​
=v
p
​
−v
t
​
=10−8=2km/h
Time taken by the policeman to catch the thief:

Time=
v
rel
​

Distance
​
=
2
0.1
​
=0.05hours
Distance run by the thief in this time:

Distance
thief
​
=v
t
​
×Time=8×0.05=0.4km
Converting to metres:

Distance
thief
​
=0.4×1000=400metres