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. 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 Felipe's distance

Use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 400$ and $b = 256$. So $c=\sqrt{400^{2}+256^{2}}=\sqrt{160000 + 65536}=\sqrt{225536}=474.9$ feet.

Step3: Let Saul's speed be $s = 3$ feet - per - second. Calculate Saul's time

Time $t=\frac{d}{s}$, for Saul, $t_{Saul}=\frac{656}{3}$ seconds.

Step4: Calculate Felipe's speed

Since Felipe and Saul finish at the same time, for Felipe, $s_{Felipe}=\frac{d_{Felipe}}{t_{Saul}}=\frac{474.9}{\frac{656}{3}}=\frac{474.9\times3}{656}\approx2.2$ feet per second.

Answer:

$2.2$