The relationship between speed $R$ and time $T$ is given as an inverse variation, which can be expressed mathematically as:

$R \cdot T = k$

where $k$ is a constant.

Step 1: Find the constant $k$

From the given data, when $R = 57 \, \text{mph}$ and $T = 8 \, \text{seconds}$, substitute these values into the formula:

$57 \cdot 8 = k$

$k = 456$

Step 2: Calculate the speed $R$ for $T = 9 \, \text{seconds}$

Using the relationship $R \cdot T = k$, substitute $k = 456$ and $T = 9$ seconds:

$R \cdot 9 = 456$

Solve for $R$:

$R = \frac{456}{9} = 50.67 \, \text{mph}$

Final Answer:

The speed of the car is approximately 50.67 mph.

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Would you like a detailed explanation or further examples?

Here are 5 related questions to expand your understanding:

1. What would the speed be if the car took 10 seconds to cover the same distance?
2. How does the graph of $R$ versus $T$ look for inverse variation?
3. If the time is halved, what happens to the speed?
4. What is the distance between the two markings based on this data?
5. How can this method be implemented for speed enforcement in various weather conditions?

Tip: Remember, in inverse variation, if one variable increases, the other decreases proportionally.