Question: Helen rented a kayak at the lake. There is a charge of $8$ as an initial fee and then $8$ an hour for every hour that she uses the kayak. If the total charge is $20$, how many hours did she kayak?
1. **State the problem:** Helen rents a kayak with an initial fee plus an hourly charge. The total cost is $20$. We need to find the number of hours she kayaked.
2. **Define variables and formula:** Let $h$ be the number of hours Helen kayaked.
The total charge $T$ is given by:
$$T = \text{initial fee} + (\text{hourly rate} \times h)$$
Given:
- Initial fee = $8$
- Hourly rate = $8$
- Total charge $T = 20$
So,
$$20 = 8 + 8h$$
3. **Solve for $h$:**
Subtract $8$ from both sides:
$$20 - 8 = 8h$$
$$12 = 8h$$
Divide both sides by $8$:
$$\frac{12}{8} = h$$
Show cancellation:
$$h = \frac{\cancel{12}}{\cancel{8}} \times \frac{3}{2}$$
Simplify fraction:
$$h = \frac{3}{2} = 1.5$$
4. **Interpretation:** Helen kayaked for $1.5$ hours, or 1 hour and 30 minutes.
**Final answer:**
$$\boxed{1.5 \text{ hours}}$$