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Part 1
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 = l150-20tl. At what times is she 90 ft from you?
To find the times at which your friend is 90 feet away from you, we need to solve the equation:
d = 150 - 20t
Set d equal to 90 and solve for t:
90 = 150 - 20t
Subtracting 150 from both sides:
-60 = -20t
Dividing both sides by -20:
3 = t
So, your friend is 90 feet away from you at t = 3 seconds.
To find the times when your friend is 90 ft away from you, we can substitute the value of d = 90 in the given equation d = 150 - 20t.
150 - 20t = 90
Now we can solve this equation for t.
Step 1: Subtract 150 from both sides of the equation:
150 - 150 - 20t = 90 - 150
-20t = -60
Step 2: Divide both sides of the equation by -20 to isolate t:
(-20t) / -20 = (-60) / -20
t = 3
So, when t = 3 seconds, your friend is 90 ft away from you.
To find the times when your friend is 90 ft away from you, we need to solve the equation d = 90.
Given the equation relating distance (d) and time (t) as d = 150 - 20t, we substitute d with 90:
90 = 150 - 20t
To solve for t, we need to isolate the variable t on one side of the equation.
20t = 150 - 90
20t = 60
Now, divide both sides of the equation by 20:
t = 60/20
t = 3
Therefore, the time when your friend is 90 ft away from you is at 3 seconds.