A policeman follows a thief, who is 840 meters ahead of him. The thief and the policeman run at a speed of 7.5 km/h and 9 km/h, respectively. What distance (in km) is run by the thief before he is nabbed by the policeman?

Initial distance separating them =840 m=
1000
840
​
=0.84 km.

Since both are running in the same direction, we compute the relative speed:

Relative Speed=Speed of Policeman−Speed of Thief
Relative Speed=9−7.5=1.5 km/h
Time (t) taken by the policeman to catch the thief:

t=
Relative Speed
Initial Distance
​
=
1.5
0.84
​
 hours
The distance run by the thief during this time period is:

Distance=Speed of Thief×t
Distance=7.5×
1.5
0.84
​

Distance=5×0.84=4.2 km
Hence, the thief runs 4.2 km before being caught.