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. start 400 feet 256 feet 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 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.

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

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

Step3: Calculate Felipe's distance

Use the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$ for the right - triangle formed by the sides of the rectangle, where $a = 400$ and $b = 256$. So $c=\sqrt{400^{2}+256^{2}}=\sqrt{160000 + 65536}=\sqrt{225536}=474.9$.

Step4: Calculate Felipe's speed

Since Felipe and Saul have the same time $t = 82$ seconds, and Felipe's distance $d = 474.9$ feet. Using $v=\frac{d}{t}$, we get $v=\frac{474.9}{82}\approx5.8$ feet per second. Rounding to the nearest tenth, the answer is $5.0$ feet per second.

Answer:

5.0