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=l 150 -20t l At what times is she 90 ft from you?
To find the times at which your friend is 90 ft away from you, we need to solve the equation d = 90.
Substituting d = 90 into the given equation, we have:
|150 - 20t| = 90
Since the distance cannot be negative, we can drop the absolute value signs:
150 - 20t = 90 or 150 - 20t = -90
Solving the first equation, we have:
150 - 20t = 90
-20t = 90 - 150
-20t = -60
t = -60 / -20
t = 3
Solving the second equation:
150 - 20t = -90
-20t = -90 - 150
-20t = -240
t = -240 / -20
t = 12
So, your friend is 90 ft away from you at t = 3 seconds and t = 12 seconds.
To find the times when your friend is 90 ft away from you, we can substitute the value for d into the given equation and solve for t.
Given: d = 150 - 20t
We want to find the values of t when d = 90.
Substitute d = 90 into the equation:
90 = 150 - 20t
To solve for t, we need to rearrange the equation:
20t = 150 - 90
Simplify the right-hand side of the equation:
20t = 60
Now divide both sides of the equation by 20:
t = 60/20
Simplify the expression:
t = 3
Hence, your friend is 90 ft away from you at t = 3 seconds.
To find the times when your friend is 90 ft away from you, we need to solve the equation:
d = 90
Given that the distance function is:
d = 150 - 20t
We substitute d = 90 into the equation:
90 = 150 - 20t
Now, let's solve for t:
20t = 150 - 90
20t = 60
t = 60 / 20
t = 3
So, your friend is 90 ft away from you at t = 3 seconds.