Let's break down the given problem step by step.
First, we know that Carys earns at a rate of [tex]$10 per hour. This information is crucial to solve the given questions.
### How many dollars does Carys earn per hour?
According to the problem, Carys earns $[/tex]10 for each hour she works. Therefore:
[tex]\[ \text{Carys earns 10 dollars per hour.} \][/tex]
### How many hours does it take Carys to earn one dollar?
To find out how many hours it takes for Carys to earn one dollar, we need to determine the fraction of an hour it would take for her to accumulate [tex]$1 at the given rate. Essentially, we are looking for \( h \) when \( E = 1 \) in the equation \( E = 10h \).
Here's the process:
1. Start with the earnings equation:
\[ E = 10h \]
2. Set \( E \) (earnings) to $[/tex]1 because we want to know the time required to earn [tex]$1:
\[ 1 = 10h \]
3. Solve for \( h \) by dividing both sides of the equation by 10:
\[ h = \frac{1}{10} \]
4. Simplifying this, we find:
\[ h = 0.1 \]
Thus, it takes Carys 0.1 hours to earn one dollar.
So, at a rate of $[/tex]10 per hour, Carys earns one dollar in:
[tex]\[ 0.1 \text{ hours} \][/tex]
Let's summarize:
- Carys earns $10 per hour.
- At that rate, it takes 0.1 hours for Carys to earn one dollar.
Thus, the answer is [tex]\( \boxed{0.1} \)[/tex] hours.
