Your friend rides his bike toward you and then passes by you at a constant speed. His distance d (in feet) from you t seconds after he started riding his bike is given by d= 200 - 18t. What does the 200 in the equation represent? What does the 18 in the equation represent? At what time(s) is he 120 ft from you?
at t=0, d=200
That is the starting distance
you know what the 18 is.
Find t when 200-18t = 120
In the equation d = 200 - 18t,
The 200 represents the initial distance between your friend and you. It is the distance when t is equal to 0, indicating the starting point.
The 18 represents the rate at which your friend is moving. It is the speed at which he is approaching you, measured in feet per second.
To find the time(s) when he is 120 ft from you, we can set d equal to 120 and solve for t:
120 = 200 - 18t
Rearranging the equation:
18t = 200 - 120
18t = 80
Dividing both sides by 18:
t = 80/18
Simplifying the fraction:
t ≈ 4.444
So, he is approximately 120 ft from you at around 4.444 seconds after he started riding his bike.
In the given equation d = 200 - 18t, we can break it down to understand what each part represents:
- The constant term 200 represents the initial distance (in feet) between you and your friend when he started riding his bike. It means that when t = 0 (at the starting time), your friend is initially 200 feet away from you.
- The coefficient 18 represents the rate at which the distance between you and your friend is changing over time. In this case, since the coefficient is negative, it indicates that your friend is moving towards you (assuming you are the reference point), and the distance decreases at a constant rate of 18 feet per second.
To find the time(s) when your friend is 120 feet away from you, we can substitute d = 120 into the equation and solve for t:
120 = 200 - 18t
To isolate the t term, we subtract 200 from both sides:
-80 = -18t
Dividing both sides by -18:
t = 80/18
Simplifying the fraction:
t ≈ 4.44 seconds
Therefore, your friend is approximately 120 feet away from you at around 4.44 seconds after he started riding his bike.