A car travels from Nairobi to Busia and back to Nairobi. If the distance between Nairobi and Busia is 400 km and the car's average speed is 120 km/h, how long did the entire journey take?

The distance between Nairobi and Busia is 400 km. For the car to leave Nairobi and arrive back in Nairobi, it must complete a round trip.

$$\text{Total Distance} = \text{Distance (Nairobi to Busia)} + \text{Distance (Busia to Nairobi)}$$ $$\text{Total Distance} = 400 \text{ km} + 400 \text{ km}$$ $$\text{Total Distance} = 800 \text{ km}$$

The formula for time is:

$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

Given the car's average speed is 120 km/h.

$$\text{Time} = \frac{800 \text{ km}}{120 \text{ km/h}}$$ $$\text{Time} = \frac{80}{12} \text{ hours}$$

Simplify the fraction:

$$\text{Time} = \frac{20}{3} \text{ hours}$$

$$\frac{20}{3} \text{ hours} = 6 \frac{2}{3} \text{ hours}$$

To convert the fractional part to minutes:

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

So, the total travel time is 6 hours and 40 minutes.

The car left Nairobi at 8:30 am.

$$\text{Arrival Time} = \text{Departure Time} + \text{Travel Time}$$ $$\text{Arrival Time} = 8:30 \text{ am} + 6 \text{ hours } 40 \text{ minutes}$$

Adding the hours: $8 + 6 = 14$ hours.
Adding the minutes: $30 + 40 = 70$ minutes.
Since 70 minutes is 1 hour and 10 minutes, we add this to the hours:
$14 \text{ hours} + 1 \text{ hour } 10 \text{ minutes} = 15 \text{ hours } 10 \text{ minutes}$
Converting to 12-hour format (pm):
$15:10$ is $3:10 \text{ pm}$.