AA.16 Solve one-step equations: word problems

Question

BXY
You've won a new prize!
Go to your game board.

While on vacation, Nate and his family visit Mount Rushmore in South Dakota. They watch a movie in the visitor center for
1
4
of an hour. This accounts for
1
5
of the total time they spend at Mount Rushmore.
Which equation can you use to find the total amount of time t Nate's family spends at Mount Rushmore?
Solve this equation for t to find the total amount of time Nate's family spends at Mount Rushmore.
To write a fraction, use a slash ( / ) to separate the numerator and denominator.
hours

Answer 1

To find the total amount of time \( t \) that Nate's family spends at Mount Rushmore, we use the information given in the problem.

They watch a movie for \( \frac{1}{4} \) of an hour, which accounts for \( \frac{1}{5} \) of the total time spent at Mount Rushmore.

We can set up the equation using the relationship between the part and the whole: \[ \frac{1}{5}t = \frac{1}{4} \]

Now, to solve for \( t \), we can multiply both sides of the equation by 5 to eliminate the fraction on the left side: \[ t = 5 \times \frac{1}{4} \]

Calculating the right side: \[ t = \frac{5}{4} \text{ hours} \]

To convert \( \frac{5}{4} \) into hours and minutes, we can convert it to a mixed number: \[ \frac{5}{4} = 1 \frac{1}{4} \text{ hours} \] This means Nate's family spends 1 hour and 15 minutes at Mount Rushmore.

Therefore, the total amount of time \( t \) that Nate's family spends at Mount Rushmore is: \[ \frac{5}{4} \text{ hours} \quad \text{or} \quad 1.25 \text{ hours} \]