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)?

To find the speed of the thief's bike, we can analyze the relative distances traveled by the thief and the police car in the same amount of time.

Let's first write down the given information:
- Initial distance between the police car and the thief = 250 m = 0.25 km
- Distance run by the thief before being caught = 1.5 km
- Speed of the police car = 70 km/h

Since the police car was 250 m (0.25 km) behind the thief when the chase started, the total distance traveled by the police car to catch the thief is:
$\text{Distance traveled by police}=\text{Initial separation}+\text{Distance run by thief}$
$\text{Distance traveled by police}=0.25\text{km}+1.5\text{km}=1.75\text{km}$

Both the police car and the thief travel for the exact same duration of time (say, $t$ hours) from the start of the chase until the thief is caught.

Using the relationship $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$, we can equate the time taken by both:
$t_{\text{police}}=t_{\text{thief}}$
$\frac{d_{\text{police}}}{s_{\text{police}}}=\frac{d_{\text{thief}}}{s_{\text{thief}}}$

Let the speed of the thief's bike be $v$ km/h. Substituting the known values into the equation:
$\frac{1.75}{70}=\frac{1.5}{v}$

Now, we solve for $v$:
$v=\frac{1.5\times 70}{1.75}$
$v=\frac{105}{1.75}$
To simplify the division, we can multiply both the numerator and the denominator by 100:
$v=\frac{10500}{175}$
Simplifying the fraction:
$v=60\text{km/h}$

Thus, the speed of the thief's bike is 60 km/h.