A policeman chases a thief. The speeds of the policeman and the thief are 8 km/h and 6 km/h, respectively. If the policeman started 10 minutes late, at what distance would he catch the thief?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 4 km.
Speed of policeman = 8 km/hr, Speed of thief = 6 km/hr
Time delay for the policeman = 10 min = 10/60 hours = 1/6 hours
We know that,
⇒ Speed = Distance/Time
Distance covered by the thief in 10 min
⇒ Distance = 6 × 1/6 = 1 km
Now,
Relative speed = Speed of policeman - Speed of theif
⇒ 8km - 6km = 2 km
The policeman has to cover the 1 km head start of the thief at a relative speed of 2 km/h
Time taken by a policeman to catch the thief = Distance/Relative speed
⇒ 1/2 = 0.5 ours = 30 minutes
The distance at which the policeman catches the thief
Distance = 8 × 0.5 = 4 km
Hence,
The policeman will catch the thief at a distance of 4 km