To determine whether the statement is true or false, we need to analyze the conditions given:
1. Vehicle 1 Speed: 60 mph
2. Vehicle 2 Speed: 50 mph
3. Passing Time: 6 to 9 seconds
First, we calculate the relative speed between the two vehicles. This is done by subtracting the speed of the slower vehicle (Vehicle 2) from the speed of the faster vehicle (Vehicle 1).
Relative Speed:
[tex]\[ \text{Relative Speed} = \text{Speed of Vehicle 1} - \text{Speed of Vehicle 2} \][/tex]
[tex]\[ \text{Relative Speed} = 60 \text{ mph} - 50 \text{ mph} = 10 \text{ mph} \][/tex]
Next, we convert the passing time from seconds to hours. This is because the speeds given are in miles per hour, and we need consistent units to calculate the distance.
Conversion from seconds to hours:
[tex]\[ \text{Time in hours (min)} = \frac{6 \text{ seconds}}{3600 \text{ seconds/hour}} = 0.00167 \text{ hours (approx)} \][/tex]
[tex]\[ \text{Time in hours (max)} = \frac{9 \text{ seconds}}{3600 \text{ seconds/hour}} = 0.0025 \text{ hours} \][/tex]
Now, we calculate the distance covered during the passing process. We use the formula:
[tex]\[ \text{Distance} = \text{Speed} \times \text{Time} \][/tex]
For the minimum passing time of 6 seconds:
[tex]\[ \text{Distance (min)} = 10 \text{ mph} \times 0.00167 \text{ hours} = 0.01667 \text{ miles (approx)} \][/tex]
For the maximum passing time of 9 seconds:
[tex]\[ \text{Distance (max)} = 10 \text{ mph} \times 0.0025 \text{ hours} = 0.025 \text{ miles} \][/tex]
Thus, the distances calculated show that at a relative speed of 10 mph, the vehicle covers between approximately 0.01667 miles and 0.025 miles in the passing time of 6 to 9 seconds.
Therefore, the statement that it takes about 6-9 seconds to pass another vehicle traveling at 50 mph when you are driving at 60 mph is supported by this analysis.
Conclusion: A. true
