Let's break down each scenario based on the formula $d = r \cdot t$, where:

• $d$ represents the distance traveled,
• $r$ represents the rate (speed),
• $t$ represents the time taken.

Now, let's find formulas for different quantities.

1. Rate ( $r$ )

To find the formula for the rate $r$, solve the equation $d = r \cdot t$ for $r$:

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

This formula shows that the rate is the distance traveled divided by the time.

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2. Time ( $t$ )

To find the formula for time $t$, solve $d = r \cdot t$ for $t$:

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

This formula shows that time is the distance traveled divided by the rate.

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Summary of Formulas:

1. Distance: $d = r \cdot t$
2. Rate: $r = \frac{d}{t}$
3. Time: $t = \frac{d}{r}$

Would you like more details on any specific scenario? Here are 5 additional questions you could explore:

1. If the distance is 150 miles and the time is 3 hours, what is the rate?
2. How long will it take to travel 300 miles at a speed of 60 miles per hour?
3. If a car is moving at 70 miles per hour, how far will it travel in 5 hours?
4. How does the formula change if the rate is not constant?
5. How can you express time in terms of rate and a given constant distance?

Tip: Always check the units for consistency when using these formulas. For example, if distance is in kilometers, ensure rate and time are also in compatible units (e.g., kilometers per hour and hours).