Question

Runners A, B, and C run a 100-m race, each at a constant speed. Runner A takes first place, beating runner B by 12 m . Runner B takes second place, beating runner C by 12 m .

By what time interval does runner A beat runner C? Express you answer as a fraction of the time that the runner A spent to finish the race.

Express your answer using two significant digits.

Answer 1

Runner A beats Runner C by the same time it takes for Runner A to finish the race.

Step-by-step explanation:

Runner A beats Runner B by 12 meters and Runner B beats Runner C by 12 meters. To find the time interval by which Runner A beats Runner C, we can set up a proportion using their speeds. Let's assume that the time it takes for Runner A to finish the race is represented by 'x'.

Since the distances are directly proportional to the times, we can write:

12 meters / x = 24 meters / (x + t), where 't' represents the time interval by which Runner A beats Runner C. Cross-multiplying, we get 12(x + t) = 24x. Expanding and simplifying, we have 12t = 12x, which simplifies to t = x.

Therefore, Runner A beats Runner C by the same time it takes for Runner A to finish the race. The time interval is equal to the time taken by Runner A to complete the race.