A and B travel the same distance at speeds of 8 km/h and 12 km/h, respectively. If B takes 30 minutes less than that taken by A. what is the distance (in km) travelled by each one of them?

Let's assume the distance travelled by each one of them is 'd' km.

Let's assume the time taken by A to cover the 'd' km distance is 't' hour.

$$\frac{d}{8}\ =\ t$$

d = 8t    Eq.(i)

B takes 30 minutes less than that taken by A.

time taken by B = $$\left(t-\frac{30}{60}\right)$$ [here we converted the given unit into hours.]

= $$\left(t-0.5\right)$$

So for B ==> $$\frac{d}{12}\ =\ (t-0.5)$$

d = 12(t-0.5)    Eq.(ii)

Equating Eq.(i) and Eq.(ii).

8t = 12(t-0.5)

2t = 3(t-0.5)

2t = 3t-1.5

3t-2t = 1.5

t = 1.5

Put the value of 't' in Eq.(i).

d = $$8\times1.5$$

Distance (in km) travelled by each one of them = d = 12 km