To solve for the distance covered by a car traveling at a speed of [tex]\( 105 \frac{1}{5} \text{ km/h} \)[/tex] over a period of 3 hours, we will use the fundamental formula that relates speed, distance, and time:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]
Let's follow the steps:
1. Identify the given values:
- Speed of the car: [tex]\( 105 \frac{1}{5} \text{ km/h} \)[/tex]
- Time: [tex]\( 3 \text{ hours} \)[/tex]
2. Convert the mixed number to an improper fraction or a decimal:
- The speed is given as [tex]\( 105 \frac{1}{5} \text{ km/h} \)[/tex].
- First, convert [tex]\( 105 \frac{1}{5} \)[/tex] to a decimal. [tex]\(\frac{1}{5} = 0.2\)[/tex].
- Thus, [tex]\( 105 \frac{1}{5} = 105 + 0.2 = 105.2 \text{ km/h} \)[/tex].
3. Apply the speed and time values into the distance formula:
- Substitute the speed [tex]\( 105.2 \text{ km/h} \)[/tex] and time [tex]\( 3 \text{ hours} \)[/tex] into the formula:
[tex]\[ \text{Distance} = 105.2 \text{ km/h} \times 3 \text{ hours} \][/tex]
4. Calculate the distance:
- Multiply the speed by the time:
[tex]\[ \text{Distance} = 105.2 \times 3 = 315.6 \text{ km} \][/tex]
Therefore, the distance covered by the car in 3 hours is [tex]\( 315.6 \text{ km} \)[/tex].
