Sure! Let's break down the problem step by step.
### Part (a)
The car travels at a constant speed of 72 km/h.
#### (i) Distance traveled in 40 minutes.
1. Convert the time from minutes to hours:
40 minutes is equal to [tex]\(\frac{40}{60}\)[/tex] hours.
2. Calculate the distance:
- Distance [tex]\(D\)[/tex] is given by the formula: [tex]\( D = \text{Speed} \times \text{Time} \)[/tex]
- Speed = 72 km/h
- Time = [tex]\(\frac{40}{60}\)[/tex] hours [tex]\(= \frac{2}{3}\)[/tex] hours
Therefore,
[tex]\[
D = 72 \times \frac{2}{3} = 48 \text{ km}
\][/tex]
So, the car travels [tex]\(\boxed{48 \text{ km}}\)[/tex] in 40 minutes.
#### (ii) Time taken to travel 126 km.
1. Calculate the time in hours:
- Time [tex]\(T\)[/tex] is given by the formula: [tex]\( T = \frac{\text{Distance}}{\text{Speed}} \)[/tex]
- Distance = 126 km
- Speed = 72 km/h
Therefore,
[tex]\[
T = \frac{126}{72} = 1.75 \text{ hours}
\][/tex]
2. Convert the time from hours to minutes:
- 1 hour = 60 minutes
- Thus, 1.75 hours = [tex]\(1.75 \times 60\)[/tex] minutes
Hence,
[tex]\[
1.75 \times 60 = 105 \text{ minutes}
\][/tex]
So, the car takes [tex]\(\boxed{105 \text{ minutes}}\)[/tex] to travel 126 km.
### Part (b)
Another car travels 196 km in 2 hours and 27 minutes.
1. Convert the time from hours and minutes to hours only:
- 27 minutes is equal to [tex]\(\frac{27}{60}\)[/tex] hours [tex]\(= 0.45\)[/tex] hours.
- Total time = 2 hours + 0.45 hours = 2.45 hours.
2. Calculate the average speed:
[tex]\[
\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}
\][/tex]
- Total Distance = 196 km
- Total Time = 2.45 hours
Therefore,
[tex]\[
\text{Average Speed} = \frac{196}{2.45} \approx 80 \text{ km/h}
\][/tex]
So, the average speed of the car is [tex]\(\boxed{80 \text{ km/h}}\)[/tex].
This completes the detailed step-by-step solution for the given questions.
