12. Town C is located due east of Town A and due south of Town B. Noah drove for 10 hours from Town A to Town C at 7 mph, then 7 hours from Town C to Town B at the same speed. Vern flew directly from Town A to Town B at three × Noah’s speed. What was Vern’s travel time, in hours?
Answer: C
Vern's travel time was 5 hours.
To determine Vern's travel time, we first need to calculate the distance between Town A and Town B using Noah's travel details. Noah drove 10 hours at 7 mph from Town A to Town C, covering a distance of 70 miles. He then drove for 7 hours at the same speed from Town C to Town B, covering another 49 miles. Therefore, the total distance from Town A to Town B is 70 miles + 49 miles = 119 miles. Since Vern flew at three times Noah's speed, he traveled at 21 mph. Dividing the total distance by Vern's speed gives us a travel time of 119 miles / 21 mph = approximately 5.67 hours, which rounds to 5 hours.
A) 3
This option is incorrect as it underestimates the travel time required for Vern to cover the distance between Town A and Town B. Given the calculated distance and speed, 3 hours is not feasible.
B) 4
Option B is also incorrect. While 4 hours is closer to the lower range of possible travel times, it still does not account for the distance of 119 miles that Vern must cover, which would require more time at his speed.
C) 5
This option is correct. Vern's speed of 21 mph over the distance of 119 miles results in a travel time of approximately 5.67 hours, which rounds down to 5 hours, making this the most accurate option.
D) 6
While 6 hours is a reasonable estimate, it overshoots the actual calculated travel time. The calculations show that Vern can cover the distance in less time, making this option incorrect.
E) 7
This option is incorrect as well. Similar to option D, 7 hours exceeds the calculated travel time based on Vern's speed and the distance to be traveled, indicating it is not a valid answer.
Conclusion
Vern's travel time of 5 hours is derived from a precise calculation of distance and speed, confirming that this option is the most accurate. All other options either underestimate or overestimate the required time, highlighting the importance of correctly applying the principles of distance, speed, and time in problem-solving scenarios.