To calculate the speed of a car that travels a given distance in a specific amount of time, we use the formula for average speed:
[tex]\[ \bar{v} = \frac{d}{t} \][/tex]
where:
- [tex]\(\bar{v}\)[/tex] is the average speed,
- [tex]\(d\)[/tex] is the distance traveled,
- [tex]\(t\)[/tex] is the time taken.
In this problem, the car travels a distance of 540 kilometers in a time of 6 hours. Let’s substitute these values into the formula:
[tex]\[ \bar{v} = \frac{540 \text{ km}}{6 \text{ hours}} \][/tex]
Now we perform the division:
[tex]\[ \bar{v} = 90 \text{ km/h} \][/tex]
Therefore, the speed of the car is [tex]\(90\)[/tex] kilometers per hour.
