To determine how many hours Richard needs to work for the week, we can set up the equation based on the information provided.
We know that Richard needs to work a total of 30 hours in a week. He has already worked \( 21.5 \) hours in the first three days.
Let \( h \) be the number of hours Richard needs to work for the remainder of the week. The equation representing the total hours worked will be:
\[ h + 21.5 = 30 \]
Now, we can solve for \( h \):
- Subtract \( 21.5 \) from both sides:
\[ h = 30 - 21.5 \]
- Calculate the right side:
\[ h = 30 - 21.5 = 8.5 \]
So, Richard needs to work \( \mathbf{8.5} \) hours to reach his total of 30 hours for the week.
Final Answer: \[ h = 8.5 \text{ hours} \]