jamie ran two laps around a track in 99 seconds. how long did it take him to run each lap if he ran the first lap 8.5m/s and the second at 8.0m/s?
Let t be the first lap time and L be the length of one lap.
8.5 m/s * t = L
8 m/s * (99-t) = L
These two equations in two unknowns can be solved for both L and t.
51 seconds
To solve the system of equations, we can use substitution or elimination method. Let's use substitution here.
From the first equation, we have L = 8.5 * t.
Substituting this value of L into the second equation, we get:
8 * (99 - t) = 8.5 * t
Multiplying out, we get:
792 - 8t = 8.5t
Adding 8t to both sides:
792 = 16.5t
Dividing both sides by 16.5:
t = 792 / 16.5
t ≈ 48 seconds
So, it took Jamie approximately 48 seconds to run the first lap.
Now, let's find the length of one lap L using the first equation:
L = 8.5 * t
L = 8.5 * 48
L ≈ 408 meters
Therefore, Jamie took approximately 48 seconds to run the first lap and the length of one lap is approximately 408 meters.