While on vacation, Tessa and her family visit Mount Rushmore in South Dakota. They watch a movie in the visitor center for \( \frac{1}{4} \) of an hour. This accounts for \( \frac{1}{5} \) of the total time they spend at Mount Rushmore. Which equation can you use to find the total amount of time \( t \) Tessa's family spends at Mount Rushmore? \[ t+\frac{1}{5}=\frac{1}{4} \] Solve this equation for \( t \) to find the total amount of time Tessa's family spends at Mount Rushmore. To wride a fraction, use a slash ( / ) to separate the numerator and denominator. Thours

To determine the total amount of time \( t \) that Tessa's family spends at Mount Rushmore, let's carefully set up and solve the equation based on the information provided. ### Understanding the Problem - **Time Watching the Movie:** \( \frac{1}{4} \) of an hour. - **This Time as a Fraction of Total Time:** The movie time accounts for \( \frac{1}{5} \) of the total time spent at Mount Rushmore. ### Setting Up the Equation Since the movie time (\( \frac{1}{4} \) hour) is \( \frac{1}{5} \) of the total time (\( t \)), we can express this relationship as: \[ \frac{1}{5}t = \frac{1}{4} \] ### Solving for \( t \) To find \( t \), follow these steps: 1. **Isolate \( t \) by multiplying both sides of the equation by 5:** \[ t = 5 \times \frac{1}{4} \] 2. **Perform the multiplication:** \[ t = \frac{5}{4} \] 3. **Convert to a mixed number (optional):** \[ t = 1 \frac{1}{4} \text{ hours} \] ### Final Answer The total amount of time Tessa's family spends at Mount Rushmore is: \[ t = \frac{5}{4} \text{ hours} \] Or equivalently: \[ t = 1 \frac{1}{4} \text{ hours} \]