To solve these questions, let's start with the first one regarding the rearrangement of the formula \( d = rt \).
Question 1: The formula \( d = rt \) can be rearranged to solve for time (t) by isolating \( t \). To do this, divide both sides by \( r \):
\[ t = \frac{d}{r} \]
So, the correct response is: A \( t = \frac{d}{r} \)
Question 2: Now, we need to find out how many hours Katie will be traveling on the train.
Given:
- Distance \( d = 405 \) miles
- Rate \( r = 90 \) miles per hour
Using the formula we rearranged:
\[ t = \frac{d}{r} = \frac{405 \text{ miles}}{90 \text{ miles per hour}} \]
Calculating this:
\[ t = \frac{405}{90} = 4.5 \text{ hours} \]
Thus, the correct response is: B \( 4.5 \text{ hours} \)
In summary, for Question 1, the answer is A, and for Question 2, the answer is B.