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 represent the total number of hours Richard needs to work for the week, you can set up the equation as follows:

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

Now, let's convert \(21 \frac{1}{5}\) into an improper fraction:

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

Now, we can rewrite the equation:

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

To isolate \(h\), subtract \(\frac{106}{5}\) from both sides. First, let's 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:

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

Subtract \(\frac{106}{5}\) from both sides:

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

Now, convert \(\frac{44}{5}\) back to a mixed number:

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

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