Two vehicles start at 8:30 a.m. and travel towards each other over a distance of 240 km. If their speeds are 80 km/h and 60 km/h, when will they meet?

Since they are moving towards each other, their speeds add up.

$$\text{Relative speed} = \text{Speed of pick-up} + \text{Speed of lorry}$$ $$\text{Relative speed} = 80 \text{ km/h} + 60 \text{ km/h}$$ $$\text{Relative speed} = 140 \text{ km/h}$$

$$\text{Time} = \frac{\text{Distance}}{\text{Relative speed}}$$ $$\text{Time} = \frac{240 \text{ km}}{140 \text{ km/h}}$$ $$\text{Time} = \frac{24}{14} \text{ hours} = \frac{12}{7} \text{ hours}$$

$$\text{Time} = 1 \frac{5}{7} \text{ hours}$$

To convert $\frac{5}{7}$ hours to minutes:

$$\frac{5}{7} \times 60 \text{ minutes} = \frac{300}{7} \text{ minutes} \approx 42.86 \text{ minutes}$$

Rounding to the nearest minute, this is approximately $43 \text{ minutes}$.
So, the time taken to meet is approximately $1 \text{ hour}$ and $43 \text{ minutes}$.

Starting time: $8:30 \text{ a.m.}$
Add $1 \text{ hour}$ and $43 \text{ minutes}$:
$8:30 \text{ a.m.} + 1 \text{ hour} = 9:30 \text{ a.m.}$
$9:30 \text{ a.m.} + 43 \text{ minutes} = 10:13 \text{ a.m.}$

The time that the lorry and the pick-up met is $10:13 \text{ a.m.}$.