Question

Starting from 200 ft away, your friend skates toward you and then passes you. She skates at a constant speed of 20 ft/s. Her distance d from you in feet after t seconds is given by d=|200-20t|. At what times is she 60 ft from you?

Answer 1

Your friend is 60 ft away from you at 7 seconds and 13 seconds.

Explanation

The distance of your friend $d$ from you in feet after $t$ seconds is given by.....

$d= |200-20t|$

When the distance of your friend is 60 ft from you, then $d= 60$. So....

$60=|200-20t|$

While solving an absolute equation, we will take two cases - one for positive and another for negative. So....

$60= 200-20t\\ \\ 60-200= -20t\\ \\ -140=-20t\\ \\ t= \frac{-140}{-20}=7$

and

$-60=200-20t\\ \\ -60-200=-20t\\ \\ -260=-20t\\ \\ t=\frac{-260}{-20}=13$

Thus, your friend is 60 ft away from you at 7 seconds and 13 seconds.