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'll follow a step-by-step approach.
### Step 1: Understand the given data
We have:
- Speed of the car: [tex]\(105 \frac{1}{5} \, \text{km/h}\)[/tex]. This is a mixed number that can be converted to an improper fraction for easier manipulation.
- Time traveled: 3 hours.
### Step 2: Convert the speed to an improper fraction
First, let's convert the mixed number [tex]\(105 \frac{1}{5}\)[/tex] to an improper fraction.
[tex]\[
105 \frac{1}{5} = 105 + \frac{1}{5}
\][/tex]
Convert 105 to a fraction with a common denominator of 5:
[tex]\[
105 = \frac{105 \times 5}{5} = \frac{525}{5}
\][/tex]
Now add [tex]\(\frac{525}{5}\)[/tex] and [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[
105 \frac{1}{5} = \frac{525}{5} + \frac{1}{5} = \frac{526}{5}
\][/tex]
Thus, the speed in improper fraction form is [tex]\(\frac{526}{5} \, \text{km/h}\)[/tex].
### Step 3: Apply the formula [tex]\( \text{Distance} = \text{Speed} \times \text{Time} \)[/tex]
We know that:
[tex]\[
\text{Distance} = \text{Speed} \times \text{Time}
\][/tex]
Substitute the values for speed and time:
[tex]\[
\text{Distance} = \left(\frac{526}{5}\right) \times 3
\][/tex]
### Step 4: Calculate the distance
To find the distance, multiply the improper fraction by the time (3 hours):
[tex]\[
\left(\frac{526}{5}\right) \times 3 = \frac{526 \times 3}{5} = \frac{1578}{5}
\][/tex]
Now, perform the division to get the distance in kilometers:
[tex]\[
\frac{1578}{5} = 315.6
\][/tex]
### Step 5: Conclusion
The distance covered by the car in 3 hours at a speed of [tex]\(105 \frac{1}{5} \, \text{km/h}\)[/tex] is 315.6 kilometers.
Thus, the car covers a distance of [tex]\(315.6 \, \text{km}\)[/tex].
