Final answer:
After converting the time lead into hours and setting up the equation, the calculated race distance where Biden finished 8 minutes ahead of Trump is 12 miles, which does not match any of the options provided. There may be a typo in the question.
Step-by-step explanation:
To solve the problem of determining the distance of the race Joe Biden and Donald Trump ran, where Biden finished 8 minutes ahead, we need to use the speeds given in the problem and set up an equation. We know Biden runs at 10 miles per hour and Trump at 9 miles per hour.
Firstly, we must convert the time Biden finished ahead from minutes into hours since the speeds are given in miles per hour. There are 60 minutes in an hour, so 8 minutes is 8/60 hours, which simplifies to 2/15 hours.
Let's denote the distance of the race as d miles. Biden would take d/10 hours to finish the race, and Trump would take d/9 hours.
Since Biden finished 2/15 hours before Trump, we can set up the equation:
d/9 - d/10 = 2/15
To solve this equation, first, find a common denominator for the fractions, which is 90. Rewriting the equation gives us:
(10d - 9d)/90 = 2/15
Simplifying further, we have d/90 = 2/15. To find the value of d, we multiply both sides of the equation by 90:
d = (2/15) × 90 which simplifies to d = 12.
This calculation shows that the race was 12 miles long, which is not one of the options provided in the question. If we consider the answer choices given, none of them fits the calculation. The student's choices may have been incorrect, or there might be a typo in the problem.