Chapter A.8, Problem 29AYU

To determine

To find: The speed of a moving walkway is typically about $2.5$ feet per second. Walking on such a moving walkway, it takes Karen a total of 40 seconds to travel 50 feet with the movement of the walkway and then back again against the movement of the walkway.What is Karen’s normal walking speed?

Answer to Problem 29AYU

Karen’s normal walking speed is $4.05$.

Explanation of Solution

$\frac{50}{x-2.5}+\frac{50}{x+2.5}=40 \text{sec}$

$\frac{50\left(x+2.5\right)+50\left(x-2.5\right)}{\left(x-2.5\right)\left(x+2.5\right)}=40$

$100x=40\left(x^2-6.25\right)$

$40x^2-100x-250=0$

$4x^2-10x-25=$

Therefore $x=4.05$ only positive root.