Answer to Question #322473 in Linear Algebra for Kenth Smith

Question

A and B are running on a track having 8 laps to mile. If they run in opposite directions, they meet every 20 seconds. If they run in the same direction, it requires 3 minutes for A to overtake B. Find the rate of each in feet per second.

Answer 1

1 mile is equal to 5280 feet, 1 lap is 5280/8=660 feet.

3 minutes are equal to 3$\cdot$60=180 seconds.

Let x - the rate of A in feet per second, y - the rate of B in feet per second.

$\begin{cases} (x+y) \cdot20=660, \\ (x-y) \cdot180=660 \end{cases}$

$\begin{cases} x+y=33,\\ x-y=3\cfrac{2}{3} \end{cases}$

$\begin{cases} 2x=36\cfrac{2}{3},\\ y=33-x \end{cases}$

$x =18\cfrac{1}{3},\ \ y =14\cfrac{2}{3} .$