Arithmetic

Time, Speed & Distance

Medium

A Police officer sees a chain snatcher and runs to catch her from a distance of 50 metres. When the Police officer starts chasing the chain snatcher from a distance of 50 metres, the chain snatcher is running @ 2 metres per second. At the same time the Police Officer is chasing the chain snatcher @ 4 metres per second.

Find the distance covered by the chain snatcher when the Police Officer shall be able to successfully catch her?

50 metres

60 metres

150 metres

100 metres

✅ Correct Option: 1

The police officer is 50 metres behind the chain snatcher. The chain snatcher runs at 2 m/s and the police officer runs at 4 m/s.

The police officer closes the gap at the difference of their speeds:

Gap closing speed $= 4 - 2 = 2$ m/s

The time required to close the 50 metre gap:

Time $= \dfrac{\text{Distance gap}}{\text{Gap closing speed}}$

Time $= \dfrac{50}{2} = 25$ seconds

The distance covered by the chain snatcher in 25 seconds:

Distance $= \text{Speed} \times \text{Time}$

Distance $= 2 \times 25$

Distance $= 50$ metres

At the moment of catching:

Chain snatcher position: $50 + 50 = 100$ metres from starting point
Police officer position: $0 + (4 \times 25) = 100$ metres from starting point

Therefore, the chain snatcher covers 50 metres before being caught.

2022: 8 Aug Shift 1

A and B are two points in a river. Point X and Y divide the line AB in three equal parts. Let the flow of the river is from A to B. The ratio of the time taken to row from point A to Y and from B to Y is 3 : 4. Find the ratio of the speed of the boat upstream to the flow of the river.

2023: 30 May Shift 3

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2022: 20 Aug Shift 1

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2023: 15 June Shift 2

A boy is running at a speed of $p$ km/h to cover a distance of 1 km but due to slippery ground his speed is reduced by $q$ km/h ( $p > q$ ). If he takes $r$ hours to cover the distance, which of the following condition is true:

2026: 29 May Shift 1

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2022: 20 Aug Shift 1

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Solution

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