Starting from

150 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
=|150−20|t. At what times is she
50 ft from​ you?
She is
50 ft away from you after
enter your response here

1 answer

To find the times when she is 50 ft away from you, we need to set the distance d equal to 50 ft and solve for t.

Given, d = |150 - 20t|

Setting d = 50, we have:

50 = |150 - 20t|

Now, we need to solve this equation for t.

If 150 - 20t is positive, it equals 50:

150 - 20t = 50

Subtracting 150 from both sides:

-20t = 50 - 150

-20t = -100

Dividing by -20:

t = -100 / -20

t = 5

So, if 150 - 20t is positive, she is 50 ft away from you after 5 seconds.

Now, if 150 - 20t is negative, it equals -50:

150 - 20t = -50

Subtracting 150 from both sides:

-20t = -50 - 150

-20t = -200

Dividing by -20:

t = -200 / -20

t = 10

So, if 150 - 20t is negative, she is 50 ft away from you after 10 seconds.

Therefore, she is 50 ft away from you after 5 seconds and 10 seconds.