Sophia and tyler are running around a 400-meter track. they start running from the same place, at the same time. sophia runs at a speed of 5 m/s and tyler runs at a speed of 4 m/s. how long will it take sophia to lap tyler?

We will call:

S: Runner Sophia.
T: Runner Tyler.

At the beginning the distance between both runners is 400m

At t = 1s Sophia runs 5m and Tyler 4m
At t = 2s Sophia runs 10m and Tyler 8m

and so on.

So, for example at t = 1s, the distance between both runner is:

D = 400m - 5m(the advantage of Sophia) + 4m(what Tyler recovers)

So, we can find a general equation for this matter. Knowing that the distance, velocity and time are related by this equation:



Then, the distance between both runners, at any time, is given by:



So we need to find the how long it will take Sophia to lap Tyler. This happens when D = 0:


∴
∴