9. John and Mike are participating in a long-distance bicycling event. Mike bicycled 24 miles in the first 2 hours. The distance John has bicycled over the first 11 minutes is shown in the chart. If John and Mike continue at the same rates, which statement will be true about their distances 4 hours into the event?
Answer: D
Mike will be 12 miles ahead of John.
After 4 hours, Mike will have biked a total distance of 48 miles, while John will have covered only 36 miles, leading to Mike being 12 miles ahead of John.
A) John will be 6 miles ahead of Mike.
This option is incorrect because based on the calculated distances, John will not surpass Mike's distance after 4 hours. Instead, Mike will maintain a lead over John, making this statement false.
B) John will be 12 miles ahead of Mike.
This statement is also incorrect. The calculations show that John will not be ahead of Mike at any point in the given time frame, as Mike's speed is greater, leading to Mike being ahead instead.
C) Mike will be 6 miles ahead of John.
While this option suggests that Mike is ahead, it understates his lead. The actual calculated distance shows that Mike is 12 miles ahead of John after 4 hours, making this statement inaccurate.
D) Mike will be 12 miles ahead of John.
This option is correct. Based on the calculations of their distances after 4 hours, Mike will have traveled 48 miles while John will have only traveled 36 miles, resulting in a 12-mile lead for Mike.
Conclusion
The analysis confirms that Mike is consistently ahead of John due to his faster pace over the course of the event. While options A, B, and C misrepresent the distances, option D accurately reflects the outcome based on the given rates of travel for both participants. Thus, Mike being 12 miles ahead is the only correct conclusion.