To find the average finishing time, we need to divide the total finishing time by the number of kids who finished the race.
Given:
- Number of kids who finished = 35
- Total finishing time = \( 8 \frac{2}{5} \) hours
First, convert \( 8 \frac{2}{5} \) hours into an improper fraction or a decimal.
The mixed number \( 8 \frac{2}{5} \) can be converted as follows:
\[ 8 = \frac{40}{5} \] \[ 8 \frac{2}{5} = \frac{40}{5} + \frac{2}{5} = \frac{42}{5} \]
Now, using this total time, we can calculate the average finishing time:
\[ \text{Average finishing time} = \frac{\text{Total finishing time}}{\text{Number of finishers}} = \frac{\frac{42}{5}}{35} \]
To divide \( \frac{42}{5} \) by \( 35 \), convert \( 35 \) to a fraction:
\[ 35 = \frac{35}{1} \]
Now, we divide fractions by multiplying by the reciprocal:
\[ \frac{42}{5} \div \frac{35}{1} = \frac{42}{5} \times \frac{1}{35} = \frac{42 \times 1}{5 \times 35} = \frac{42}{175} \]
Next, simplify \( \frac{42}{175} \). First, we need to find the greatest common divisor (GCD) of 42 and 175.
The prime factorization of 42 is \( 2 \times 3 \times 7 \). The prime factorization of 175 is \( 5 \times 5 \times 7 \) or \( 5^2 \times 7 \). The GCD is \( 7 \).
Now divide both the numerator and the denominator by 7:
\[ \frac{42 \div 7}{175 \div 7} = \frac{6}{25} \]
Thus, the average finishing time in hours is:
\[ \frac{6}{25} \text{ hours} \]
To convert \( \frac{6}{25} \) hours into minutes, we multiply by 60 (since there are 60 minutes in an hour):
\[ \frac{6}{25} \times 60 = \frac{6 \times 60}{25} = \frac{360}{25} = 14.4 \text{ minutes} \]
To summarize, the average finishing time is:
\[ \text{Average finishing time} = \frac{6}{25} \text{ hours} \text{ or } 14.4 \text{ minutes} \]
So the final answer is:
\[ \frac{6}{25} \text{ hours} \] or approximately 14 minutes and 24 seconds.
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