During weekdays, Richard is working as a part-time library assistant at a university. He needs to work for a total of 30 hours a week. For the first three days of the week, he worked 21 1/5

To find the number of hours \( h \) that Richard needs to work to reach a total of 30 hours for the week, we can start with the equation:

\[ h + 21 \frac{1}{5} = 30 \]

First, we need to convert \( 21 \frac{1}{5} \) into an improper fraction to make calculations easier:

\[ 21 \frac{1}{5} = \frac{21 \times 5 + 1}{5} = \frac{105 + 1}{5} = \frac{106}{5} \]

Now, substitute \( 21 \frac{1}{5} \) with \( \frac{106}{5} \) in the equation:

\[ h + \frac{106}{5} = 30 \]

Next, convert 30 into a fraction with a denominator of 5:

\[ 30 = \frac{30 \times 5}{5} = \frac{150}{5} \]

Now the equation looks like this:

\[ h + \frac{106}{5} = \frac{150}{5} \]

To isolate \( h \), subtract \( \frac{106}{5} \) from both sides:

\[ h = \frac{150}{5} - \frac{106}{5} \]

Combine the fractions:

\[ h = \frac{150 - 106}{5} = \frac{44}{5} \]

Now convert \( \frac{44}{5} \) into a mixed number:

\[ \frac{44}{5} = 8 \frac{4}{5} \]

So, the final answer is:

\[ h + 21 \frac{1}{5} = 30 \ h = 8 \frac{4}{5} \text{ hours} \]

Richard needs to work \( 8 \frac{4}{5} \) hours to reach a total of 30 hours for the week.