Step 1: Determine the distances covered by A and B.

A's distance: A covers the full 500 meters. B's distance: B starts 45 meters ahead, so B covers 500 meters minus 45 meters, which equals 455 meters.

Step 2: Calculate the ratio of the distances covered.

The ratio of the distances covered by A and B is:

Distance Ratio = A's Distance / B's Distance = $500 / 455$

Simplifying this ratio:

$500 / 455 = 100 / 91$

Step 3: Relate the distance ratio to the speed ratio.

Since both A and B start at the same time and run for the same duration, their speeds are directly proportional to the distances they cover. Therefore, the ratio of their speeds is the same as the ratio of the distances:

Speed Ratio = A's Speed / B's Speed = $100 / 91$

Step 4: Convert the ratio to a more familiar form.

To express the ratio in whole numbers, we can multiply both the numerator and the denominator by 25:

$100 / 91 * 25 / 25 = 2500 / 2275$

This simplifies to approximately 25:21.

Conclusion:

The ratio of the speeds of A to B is approximately 25:21.

Therefore, the correct answer is A. 25:21.