A policeman follows a thief who is 400m ahead of him. If they run at the speed of 7km/h and 6km/h, respectively, what distance does the policeman run to catch up with the thief?
- A2800 m
- B2700 m
- C2500 m
- D2600 m
Solution & Step-by-step Explanation
Given:
Initial distance between policeman and thief = 400m=0.4km
Speed of policeman (v
p
) = 7km/h
Speed of thief (v
t
) = 6km/h
Since they are running in the same direction, the relative speed is:
v
rel
=v
p
−v
t
=7−6=1km/h
Time (t) taken by the policeman to catch the thief:
t=
v
rel
Distance
=
1km/h
0.4km
=0.4hours
Distance run by the policeman in this time:
Distance=v
p
×t=7km/h×0.4hours=2.8km=2800m
Initial distance between policeman and thief = 400m=0.4km
Speed of policeman (v
p
) = 7km/h
Speed of thief (v
t
) = 6km/h
Since they are running in the same direction, the relative speed is:
v
rel
=v
p
−v
t
=7−6=1km/h
Time (t) taken by the policeman to catch the thief:
t=
v
rel
Distance
=
1km/h
0.4km
=0.4hours
Distance run by the policeman in this time:
Distance=v
p
×t=7km/h×0.4hours=2.8km=2800m