# 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.

## 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.