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Let's solve this problem by calculating the lower and upper bounds for speed \(s\).

### Formula and given values:
The relationship between speed \(s\), distance \(d\), and time \(t\) is:

\[
s = \frac{d}{t}
\]

The given values are:
- Distance \(d = 190\) meters (to 2 significant figures).
- Time \(t = 8.1\) seconds (to 2 significant figures).

Now, we need to calculate the lower and upper bounds for both \(d\) and \(t\).

### Step 1: Find the bounds for \(d\) and \(t\)

#### For distance \(d = 190 \, \text{meters}\):
- Lower bound of \(d\): \(d_{\text{lower}} = 185 \, \text{meters}\) (since 190 is rounded to the nearest 10, its lower bound is 185).
- Upper bound of \(d\): \(d_{\text{upper}} = 195 \, \text{meters}\).

#### For time \(t = 8.1 \, \text{seconds}\):
- Lower bound of \(t\): \(t_{\text{lower}} = 8.05 \, \text{seconds}\) (since 8.1 is rounded to the nearest 0.1, its lower bound is 8.05).
- Upper bound of \(t\): \(t_{\text{upper}} = 8.15 \, \text{seconds}\).

### Step 2: Calculate the bounds for speed \(s\)

#### Lower bound of \(s\):
\[
s_{\text{lower}} = \frac{d_{\text{lower}}}{t_{\text{upper}}} = \frac{185}{8.15} \approx 22.7 \, \text{m/s}
\]

#### Upper bound of \(s\):
\[
s_{\text{upper}} = \frac{d_{\text{upper}}}{t_{\text{lower}}} = \frac{195}{8.05} \approx 24.2 \, \text{m/s}
\]

### Final answer:
- Lower bound of \(s\) is approximately \(22.7 \, \text{m/s}\) to 3 significant figures.
- Upper bound of \(s\) is approximately \(24.2 \, \text{m/s}\) to 3 significant figures.

Would you like more details or have any questions?

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Here are some related questions you could explore:
1. How are significant figures used to determine the accuracy of the bounds?
2. What effect does rounding have on calculating the upper and lower bounds?
3. How would the bounds change if \(d\) or \(t\) were given with more significant figures?
4. How can we verify the accuracy of the calculated speed bounds?
5. How is uncertainty in measurement accounted for in these bounds?

**Tip:** When rounding to significant figures, always check if you are rounding up or down correctly as it can affect precision significantly.

A formula connecting speed (s), distance (d), and time (t) is s = d/t. d = 190 meters to 2 significant figures, t = 8.1 seconds to 2 significant figures. Calculate the lower and upper bounds of s. Give your answers to 3 significant figures.

Learn how to calculate the lower and upper bounds of speed using the formula s = d/t. This problem involves distance (190 meters), time (8.1 seconds), and understanding significant figures. Suitable for students in Grades 10-12.

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