Let's break down the problem step by step.

Given Data:

• Country lanes: Distance = 8 km, Speed = 40 km/h.
• Main road: Distance = 20 km, Speed = 50 km/h.
• Motorway: Distance = 44 km, Speed = 110 km/h.

(a) Time taken for the total journey:

We calculate the time taken for each segment using the formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

1. Time on country lanes: $\text{Time} = \frac{8 \text{ km}}{40 \text{ km/h}} = 0.2 \text{ hours} = 12 \text{ minutes}$

2. Time on main road: $\text{Time} = \frac{20 \text{ km}}{50 \text{ km/h}} = 0.4 \text{ hours} = 24 \text{ minutes}$

3. Time on motorway: $\text{Time} = \frac{44 \text{ km}}{110 \text{ km/h}} = 0.4 \text{ hours} = 24 \text{ minutes}$

Total time for the journey:

$\text{Total time} = 0.2 \text{ h} + 0.4 \text{ h} + 0.4 \text{ h} = 1.0 \text{ hours}$

(b) Average speed for the whole journey:

To find the average speed, use the formula: $\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}$

• Total distance = 8 km + 20 km + 44 km = 72 km.
• Total time = 1.0 hours (as calculated above).

Thus, the average speed is: $\text{Average speed} = \frac{72 \text{ km}}{1.0 \text{ h}} = 72 \text{ km/h}$

Final answers:

• Time taken for the total journey = 1 hour.
• Average speed for the whole journey = 72 km/h.

Would you like further details on any of these calculations or explanations?

Relative questions:

1. How would the average speed change if the speed on the motorway was higher?
2. What would happen to the total time if the distance on the country lanes increased?
3. Can you calculate the time for the journey if the speed on the main road was reduced to 40 km/h?
4. How would the average speed change if the motorway speed was doubled?
5. If the trip included a break of 10 minutes, how would that affect the total time?

Tip:

Always remember that average speed is not just the arithmetic mean of speeds over different segments but is calculated based on total distance and total time.