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.

Step-by-step 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= (-140)/(-20)=7`

and

`-60=200-20t\\ \\ -60-200=-20t\\ \\ -260=-20t\\ \\ t=(-260)/(-20)=13`

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