A car starts driving at noon (t = 0) and drives at exactly 50 miles per hour until 4pm (t = 4). (a) How far does the car drive in that time? (b) Sketch a graph of the car's speed (in miles per hour) vs its time (in hours). Shade in the area below your graph, between t = 0 and t = 4.

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### Problem Statement on Constant Speed Driving

**1. A car starts driving at noon (t = 0) and drives at exactly 50 miles per hour until 4 pm (t = 4).**

**(a) How far does the car drive in that time?**

*Solution:* 
To determine the distance driven, use the formula:

\[ \text{Distance} = \text{Speed} \times \text{Time} \]

In this case, the speed is 50 miles per hour, and the time is 4 hours (from noon to 4 pm).

\[ \text{Distance} = 50 \, \text{miles/hour} \times 4 \, \text{hours} = 200 \, \text{miles} \]

So, the car drives **200 miles** during this time period.

**(b) Sketch a graph of the car’s speed (in miles per hour) vs its time (in hours). Shade in the area below your graph, between t = 0 and t = 4.**

*Explanation:* 
The graph of the car's speed vs time is a horizontal line because the speed is constant at 50 miles per hour. The x-axis represents the time (t) in hours, and the y-axis represents the speed (s) in miles per hour.

**Drawing the Graph:**

1. Draw the time axis (horizontal) from \( t = 0 \) to \( t = 4 \).
2. Draw the speed axis (vertical) up to at least 50 miles per hour.
3. Plot a horizontal line at \( y = 50 \) from \( t = 0 \) to \( t = 4 \).

**Shaded Area:**

The area below the line (from \( t = 0 \) to \( t = 4 \)) and above the time axis represents the distance traveled. Since the car drives at a constant speed:

\[
\text{Shaded Area} = \text{Speed} \times \text{Time} = 50 \, \text{miles/hour} \times 4 \, \text{hours} = 200 \, \text{square units}
\]

This visual representation confirms that the car covers 200 miles.

**Graph Details:**

- The x-axis is labeled "Time (hours)" ranging from 0 to 4.
-
Transcribed Image Text:### Problem Statement on Constant Speed Driving **1. A car starts driving at noon (t = 0) and drives at exactly 50 miles per hour until 4 pm (t = 4).** **(a) How far does the car drive in that time?** *Solution:* To determine the distance driven, use the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] In this case, the speed is 50 miles per hour, and the time is 4 hours (from noon to 4 pm). \[ \text{Distance} = 50 \, \text{miles/hour} \times 4 \, \text{hours} = 200 \, \text{miles} \] So, the car drives **200 miles** during this time period. **(b) Sketch a graph of the car’s speed (in miles per hour) vs its time (in hours). Shade in the area below your graph, between t = 0 and t = 4.** *Explanation:* The graph of the car's speed vs time is a horizontal line because the speed is constant at 50 miles per hour. The x-axis represents the time (t) in hours, and the y-axis represents the speed (s) in miles per hour. **Drawing the Graph:** 1. Draw the time axis (horizontal) from \( t = 0 \) to \( t = 4 \). 2. Draw the speed axis (vertical) up to at least 50 miles per hour. 3. Plot a horizontal line at \( y = 50 \) from \( t = 0 \) to \( t = 4 \). **Shaded Area:** The area below the line (from \( t = 0 \) to \( t = 4 \)) and above the time axis represents the distance traveled. Since the car drives at a constant speed: \[ \text{Shaded Area} = \text{Speed} \times \text{Time} = 50 \, \text{miles/hour} \times 4 \, \text{hours} = 200 \, \text{square units} \] This visual representation confirms that the car covers 200 miles. **Graph Details:** - The x-axis is labeled "Time (hours)" ranging from 0 to 4. -
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