starting from 100 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 = |100 - 20|. At what times is she 60 ft away from you.

Question

She is 60 ft away from you after how many seconds?

Answer 1

Her distance from you, d, in feet after t seconds is given by:

d = |100 - 20t|

To find the times when she is 60 ft away from you, we can set d equal to 60 and solve for t:

60 = |100 - 20t|

Now we can solve for t by splitting the equation into two cases:

Case 1: 100 - 20t is positive

60 = 100 - 20t

Subtracting 100 from both sides gives:

-40 = -20t

Dividing by -20 gives:

t = 2

Case 2: 100 - 20t is negative

60 = -(100 - 20t)

Distributing the negative sign gives:

60 = -100 + 20t

Adding 100 to both sides gives:

160 = 20t

Dividing by 20 gives:

t = 8

So she is 60 ft away from you after 2 seconds and 8 seconds.