A bus leaves Nakuru at 7:00 AM traveling at 60 km/h. A saloon car leaves the same town at 7:40 AM traveling at 80 km/h. When and how far from Nakuru does the saloon car catch up with the bus?

The bus traveled for 40 minutes at a speed of $60 \text{ km/h}$.
First, convert 40 minutes to hours:

$$40 \text{ minutes} = \frac{40}{60} \text{ hours} = \frac{2}{3} \text{ hours}$$

Distance covered by the bus in 40 minutes:

$$\text{Distance} = \text{Speed} \times \text{Time}$$ $$\text{Distance}_{\text{bus initial}} = 60 \text{ km/h} \times \frac{2}{3} \text{ h} = 40 \text{ km}$$

Both vehicles are moving in the same direction.
Speed of the bus ($V_B$) = $60 \text{ km/h}$
Speed of the saloon car ($V_S$) = $80 \text{ km/h}$
Relative speed ($V_R$) = $V_S - V_B$

$$V_R = 80 \text{ km/h} - 60 \text{ km/h} = 20 \text{ km/h}$$

The saloon car needs to cover the initial distance of $40 \text{ km}$ that the bus traveled.

$$\text{Time} = \frac{\text{Distance}}{\text{Relative Speed}}$$ $$\text{Time}_{\text{catch up}} = \frac{40 \text{ km}}{20 \text{ km/h}} = 2 \text{ hours}$$

The saloon car travels for 2 hours at a speed of $80 \text{ km/h}$.

$$\text{Distance}_{\text{catch up}} = \text{Speed}_{\text{saloon car}} \times \text{Time}_{\text{catch up}}$$ $$\text{Distance}_{\text{catch up}} = 80 \text{ km/h} \times 2 \text{ h} = 160 \text{ km}$$

The saloon car catches up with the bus at a distance of 160 km from Nakuru.

The total distance between the towns is 320 km. The question asks "How far from Nakuru did the saloon car catch up with the bus?".

The saloon car caught up with the bus at a distance of $\text{160 km}$.