Two motor cars are 1.2 km apart and moving in opposite directions. Car A is moving at 80 km/h due east and car B is moving at 100 km/h due west. Calculate: a) The velocity of car A relative to car B. b) The time taken for the cars to reach each other. c) The distance car A travels to reach car B.

The velocity of car A relative to car B ($v_{AB}$) is given by:

$$v_{AB} = v_A - v_B$$

$$v_{AB} = 100 \text{ km/h} - (-80 \text{ km/h})$$ $$v_{AB} = 100 \text{ km/h} + 80 \text{ km/h}$$

$$v_{AB} = 180 \text{ km/h}$$

The velocity of car A relative to car B is $\boxed{\text{180 km/h}}$.

Since the cars are moving towards each other, their relative speed of approach is the sum of their magnitudes, which is the magnitude of $v_{AB}$.

$$v_{rel} = |v_A| + |v_B| = 100 \text{ km/h} + 80 \text{ km/h} = 180 \text{ km/h}$$

$$t = \frac{1.2}{180} \text{ hours}$$ $$t = \frac{12}{1800} \text{ hours}$$ $$t = \frac{1}{150} \text{ hours}$$

To express in minutes:

$$t = \frac{1}{150} \times 60 \text{ minutes} = \frac{60}{150} \text{ minutes} = \frac{2}{5} \text{ minutes} = 0.4 \text{ minutes}$$

The time taken for the cars to reach each other is $\boxed{\text{0.4 minutes}}$ or $\boxed{\frac{1}{150} \text{ hours}}$.

$$d_A = \frac{100}{150} \text{ km}$$ $$d_A = \frac{2}{3} \text{ km}$$

The distance car A travels is $\boxed{\frac{2}{3} \text{ km}}$ or approximately $\boxed{\text{0.667 km}}$.