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 = l200-20l. At what times is she 160 ft from you?

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 = l200-20l. At what times is she 160 ft from you?

Answer 1

We can solve for the times at which she is 160 ft from you by setting the equation d = |200 - 20t| equal to 160 and solving for t.

|200 - 20t| = 160

To simplify the equation, we can consider two cases separately:
1. When 200 - 20t is positive:
200 - 20t = 160
-20t = -40
t = 2 seconds

2. When 200 - 20t is negative:
-(200 - 20t) = 160
200 - 20t = -160
-20t = -360
t = 18 seconds

So, she is 160 ft from you at t = 2 seconds and t = 18 seconds.

Answer 2

To find the times when your friend is 160 ft away from you, we can substitute 160 ft for d in the equation d = |200 - 20t|. Then we solve for t.

Substituting 160 ft for d, we get:

160 = |200 - 20t|

To solve this equation, we will consider two cases: one when the expression inside the absolute value is positive, and the other when it's negative.

Case 1: (200 - 20t) > 0

In this case, we don't need to take the absolute value, and the equation becomes:

160 = 200 - 20t

Rearranging the terms, we get:

20t = 200 - 160
20t = 40

Dividing both sides by 20, we find:

t = 2

So, when (200 - 20t) > 0, your friend is 160 ft away from you at t = 2 seconds.

Case 2: (200 - 20t) < 0

In this case, we need to take the absolute value, and the equation becomes:

160 = -(200 - 20t)

Expanding the brackets, we get:

160 = -200 + 20t

Rearranging the terms, we have:

20t = 360

Dividing both sides by 20, we find:

t = 18

So, when (200 - 20t) < 0, your friend is 160 ft away from you at t = 18 seconds.

Therefore, your friend is 160 ft away from you at both t = 2 seconds and t = 18 seconds.

Answer 3

To find the times when she is 160 ft from you, we need to solve the equation d = |200 - 20t| = 160.

First, let's consider when the expression within the absolute value is positive:
200 - 20t = 160

Now, solve for t:
200 - 160 = 20t
40 = 20t
t = 2

Now, let's consider when the expression within the absolute value is negative:
-(200 - 20t) = 160

Multiply both sides by -1:
200 - 20t = -160

Now, solve for t:
200 + 160 = 20t
360 = 20t
t = 18

Therefore, she is 160 ft away from you at t = 2 seconds and t = 18 seconds.

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 = l200-20l. At what times is she 160 ft from​ you?

We can solve for the times at which she is 160 ft from you by setting the equation d = |200 - 20t| equal to 160 and solving for t.

To find the times when your friend is 160 ft away from you, we can substitute 160 ft for d in the equation d = |200 - 20t|. Then we solve for t.

To find the times when she is 160 ft from you, we need to solve the equation d = |200 - 20t| = 160.

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 = l200-20l. At what times is she 160 ft from you?