Question

saul and felipe are standing at the corner of a rectangular park. they will race to the opposite corner. the dimensions of the park are shown. 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. feet per second

Explanation:

Step1: Calculate Saul's total distance

Saul travels along two sides of the rectangle: $400 + 256 = 656$ feet

Step2: Find Saul's race time

Time = $\frac{\text{Distance}}{\text{Speed}}$, so $\frac{656}{8} = 82$ seconds

Step3: Calculate Felipe's path length

Use Pythagorean theorem: $\sqrt{400^2 + 256^2} = \sqrt{160000 + 65536} = \sqrt{225536} = 474.906$ feet

Step4: Find Felipe's required speed

Speed = $\frac{\text{Distance}}{\text{Time}}$, so $\frac{474.906}{82} \approx 5.8$ feet per second

Answer:

5.8 feet per second