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.
She is 60 ft away from you after how many seconds?
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.
To find the time when your friend is 60 ft away from you, we can use the given distance formula:
d = |100 - 20t|
We want to find the value of t when d is equal to 60.
Substituting this into the equation, we have:
60 = |100 - 20t|
To remove the absolute value, we can express the equation as two separate cases:
1. 60 = 100 - 20t
2. 60 = -(100 - 20t)
Solving the first case:
60 = 100 - 20t
20t = 100 - 60
20t = 40
t = 2
Solving the second case:
60 = -(100 - 20t)
60 = -100 + 20t
20t = 60 + 100
20t = 160
t = 8
Therefore, your friend is 60 ft away from you after 2 seconds and again after 8 seconds.
To find the times at which your friend is 60 ft away from you, we can substitute the value of d = 60 ft into the equation for distance:
d = |100 - 20t|
So, we have:
60 = |100 - 20t|
To simplify, we can remove the absolute value notation by considering two cases:
1. When 100 - 20t >= 0: We have 60 = 100 - 20t, which gives us t = (100 - 60) / 20 = 2 seconds.
2. When 100 - 20t < 0: In this case, the absolute value will be negative, so we negate the equation:
60 = -(100 - 20t)
60 = -100 + 20t
20t = 160
t = 8 seconds.
Therefore, your friend is 60 ft away from you at 2 seconds and at 8 seconds.