Question

A culprit was spotted by a policeman from a distance of 250 meter. When the policeman started

running towards the culprit at a speed of 10 km/h, the culprit also fled. If his speed was 8 km/h, find how far the culprit had run before he was overpowered.​

Answer 1

The culprit had run 1000m before he was overpowered.​

Let the distance travelled by the culprit be 'd' m.

So, distance covered by the policeman will be (d + 100) m.

Speed of culprit = 8 km/hr = (8000/3600) m/s = 20/9 m/s.   [1km = 1000m and 1hr = 3600s]

Speed of policeman = 10 km/hr = (10000/3600) m/s = 25/9 m/s

Time taken by culprit = (Distance travelled/Speed of culprit)

= (d/  20/9) s = (9d/20)s

Time taken by policeman = (Distance travelled/Speed of policeman)

= ([d+100]/  25/9) s = (9[d+250]/25)s

As, the time taken is the same for culprit and policeman so,

9d/20 = 9(d+250)/25

⇒d/20 = (d+250)/25

⇒25d  = 20(d+250)

⇒25d = 20d + 5000

⇒5d = 5000

⇒d = 5000/5 = 1000

So, he had run 1000m