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in Distance, Time and Speed by (240k points)
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On a road of length 90 km, a thief escapes on a motorcycle at 30 km/hr. An hour later, a policeman A starts the chase in the same direction at 70 km/hr. At the same time, another policeman B starts from opposite direction at 60 km/hr. Calculate the time taken by the policeman who will catch the thief first?


1. 60 hr
2. 45 hr
3. 60 min
4. 40 min

1 Answer

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Best answer
Correct Answer - Option 4 : 40 min

Given:

Length of road = 90 km

Speed of thief = 30 km/hr

Speed of policeman A = 70 km/hr

Speed of policeman B = 60 km/hr

Formula used:

Speed = Distance/Time

Concept used:

If speed of body A is x m/s and speed of body B is y m/s then,

Relative speed of two bodies moving in same direction = (x – y) m/s

Relative speed of two bodies moving in opposite direction = (x + y) m/s

Calculation:

When the policeman starts the chase, the thief has already covered 30 km

Relative speed of Policeman A with respect to thief = (70 – 30) km/hr

⇒ 40 km/hr

Time taken by the policeman A to catch the thief = 30/40 hr

⇒ 3/4 hr

⇒ (3 × 60)/4 min

⇒ 45 min

Relative speed of policeman B with respect to thief = 60 + 30

⇒ 90 km/hr

Time taken by the policeman B to catch the thief = 60/90 hr

⇒ 2/3 hr

⇒ (2 × 60)/3 hr

⇒ 40 min

Policeman B will catch first in 40 min.

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