A policeman chases a thief on a straight road. The policeman catches the thief in 15 minutes if he drives with a speed of 60 km/h and catches the thief in 0.5 hours if he drives with a speed 45 km/h. What should be his driving speed (in km/h) to catch the thief in just 10 minutes?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 75
Relative Speed = Speed of Policeman - Speed of Thief
Distance = Relative Speed × Time
Relative speed = 60 - x and 45 -x in two cases respectively.
Set the distances equal for both cases:
0.25(60 - x) = 0.5(45 - x)
⇒ x = 30 km/h (thief's speed)
To catch the thief in 10 minutes:
7.5 = (v - 30) × 1/6
⇒ v = 75 km/h