Let's solve each part of the problem based on the given formula $d = rt$, where:

• $d$ is the distance,
• $r$ is the rate (speed), and
• $t$ is the time.

(a) Solve the formula for $t$

We start with the equation $d = rt$. To solve for $t$, divide both sides by $r$:

$t = \frac{d}{r}$

So the formula for $t$ is $t = \frac{d}{r}$.

(b) Find the time when $d = 225$ miles and $r = 50$ miles per hour

Using the formula from part (a):

$t = \frac{225}{50} = 4.5 \text{ hours}$

So, it will take 4.5 hours to cover 225 miles at a speed of 50 miles per hour.

Would you like further details or explanations? Here are 5 related questions to extend your understanding:

1. How would the time change if the speed were reduced to 40 miles per hour?
2. What would the formula look like if you wanted to solve for $r$ instead?
3. How can this formula be used to calculate time for other units like kilometers and kilometers per hour?
4. If you traveled for 6 hours at 60 miles per hour, how far would you go?
5. Can you express the formula $t = \frac{d}{r}$ graphically for different values of $r$?

Tip: The formula $d = rt$ is linear, meaning as speed increases, time decreases for the same distance. Keep this inverse relationship in mind when solving travel problems.