Saul and Felipe are standing at the corner of a rectangular park. They will race to the opposite corner. The park is 400 ft in width 256 ft in length. They start at the top left corner and run to the bottom right corner and Saul runs at a constant rate of 8 feet per second along the sidewalk that surrounds the park. Felipe will walk at a constant rate along the path that goes straight from one corner to the other. How fast, in feet per second, must Felipe walk to finish the race at the same time as Saul? Round the answer to the nearest tenth. Enter the answer in the box.

Answer 1

In order to finish the race at the same time as Saul, Felipe must walk at a speed that allows him to cover the diagonal distance of the park in the same time it takes Saul to cover the perimeter.

The diagonal distance of the park can be calculated using the Pythagorean theorem: diagonal = sqrt(width^2 + length^2) = sqrt(400^2 + 256^2) = sqrt(160000 + 65536) = sqrt(225536) ≈ 475.3 ft.

Saul takes (400 + 256) / 8 = 656 / 8 = 82 seconds to run around the park.

Felipe must walk at a speed that allows him to cover the diagonal distance of 475.3 ft in 82 seconds. Therefore, Felipe must walk at a speed of 475.3 / 82 ≈ 5.8 ft/s.

Thus, Felipe must walk at a speed of approximately **5.8 feet per second** to finish the race at the same time as Saul.

Answer 2

confirm your answer

Answer 3

Let's confirm the answer by calculating the time it takes for Felipe to walk the diagonal distance of the park at a speed of 5.8 feet per second.

The time it takes for Felipe to walk the diagonal distance (475.3 ft) at a speed of 5.8 ft/s can be calculated as distance / speed = 475.3 / 5.8 ≈ 82 seconds.

This matches the time it takes for Saul to run around the park, which is 82 seconds.

Therefore, the confirmation is that Felipe must walk at a speed of approximately 5.8 feet per second to finish the race at the same time as Saul.