Question

Of the 42 kids who entered the race 35 finished. If the sum of all the finishing times was 8 2/5 hours, what was the average finishing time?

Answer 1

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.