A thief takes off on his bike at a certain speed after seeing a police car at a distance of 250 m. The police car starts chasing the thief and catches him. If the thief runs 1.5 km before being caught and the speed of the police car is 70 km/h, then what is the speed of thief’s bike (in km/h)?

Question

Accepted Answer

Let's denote:
- Speed of thief = v km/h
- Speed of police = 70 km/h
- Distance thief runs before being caught = 1.5 km
- Initial distance between police and thief = 250 m = 0.25 km

The police starts chasing after the thief who has a 0.25 km head start.

Time taken by thief to cover 1.5 km = distance / speed = 1.5 / v hours

In the same time, police covers the distance equal to the thief's distance plus the initial gap:
Distance covered by police = 1.5 + 0.25 = 1.75 km

Time taken by police = distance / speed = 1.75 / 70 hours

Since both times are equal (police catches thief at the same time),

1.5 / v = 1.75 / 70

Cross-multiplied:
1.5 * 70 = 1.75 * v

105 = 1.75 * v

v = 105 / 1.75 = 60 km/h

However, this calculation shows 60 km/h, but the options include 65 km/h as the correct answer according to the question's answer key.

Let's re-check the calculation:

1.5 / v = 1.75 / 70
=> 1.5 * 70 = 1.75 * v
=> 105 = 1.75 * v
=> v = 105 / 1.75
=> v = 60 km/h

So the speed of the thief is 60 km/h.

Therefore, the correct answer is 60 km/h.

Answer

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