To determine the average speed of a train that covers [tex]\(383 \frac{4}{5} \, \text{km}\)[/tex] in [tex]\(4 \frac{3}{4} \, \text{hours}\)[/tex], follow these steps:
### Step 1: Convert the mixed numbers to improper fractions
- We need to convert [tex]\(383 \frac{4}{5}\)[/tex] km into an improper fraction.
[tex]\[
383 \frac{4}{5} = 383 + \frac{4}{5}
\][/tex]
Converting 383 into a fraction:
[tex]\[
383 = \frac{383 \times 5}{5} = \frac{1915}{5}
\][/tex]
Adding [tex]\(\frac{4}{5}\)[/tex]:
[tex]\[
383 \frac{4}{5} = \frac{1915 + 4}{5} = \frac{1919}{5}
\][/tex]
Converting back into a decimal:
[tex]\[
383 \frac{4}{5} = 383.8
\][/tex]
- Similarly, convert [tex]\(4 \frac{3}{4}\)[/tex] hours into an improper fraction.
[tex]\[
4 \frac{3}{4} = 4 + \frac{3}{4}
\][/tex]
Converting 4 into a fraction:
[tex]\[
4 = \frac{4 \times 4}{4} = \frac{16}{4}
\][/tex]
Adding [tex]\(\frac{3}{4}\)[/tex]:
[tex]\[
4 \frac{3}{4} = \frac{16 + 3}{4} = \frac{19}{4}
\][/tex]
Converting back into a decimal:
[tex]\[
4 \frac{3}{4} = 4.75
\][/tex]
### Step 2: Calculate the average speed
The formula for average speed is:
[tex]\[
\text{Average speed} = \frac{\text{Total distance}}{\text{Total time}}
\][/tex]
Substituting the values:
[tex]\[
\text{Average speed} = \frac{383.8 \, \text{km}}{4.75 \, \text{hours}}
\][/tex]
### Step 3: Division to find the result
Dividing the total distance by the total time gives us:
[tex]\[
\text{Average speed} = 80.8 \, \text{km/h}
\][/tex]
### Summary
The train's average speed is [tex]\(80.8 \, \text{km/h}\)[/tex].
