Question

saul and felipe are standing at the corner of a rectangular park. they will race to the opposite corner. the dimensions are 400 feet and 256 feet. start finish 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 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 the answer in the box. feet per second

Explanation:

Step1: Calculate Saul's distance

Saul runs along the sides of the rectangle. The distance he runs is $400 + 256=656$ feet.

Step2: Calculate Saul's time

Saul's speed is 8 feet per second. Using the formula $t=\frac{d}{v}$, where $d$ is distance and $v$ is speed, his time $t=\frac{656}{8}=82$ seconds.

Step3: Calculate Felipe's distance

Use the Pythagorean theorem for the rectangle. The diagonal (Felipe's path) $d_{Felipe}=\sqrt{400^{2}+256^{2}}=\sqrt{160000 + 65536}=\sqrt{225536}=474.9$ feet.

Step4: Calculate Felipe's speed

Since Felipe and Saul take the same time, and time $t = 82$ seconds. Using the formula $v=\frac{d}{t}$, Felipe's speed $v=\frac{474.9}{82}\approx5.8$ feet per second.

Answer:

5.8