Question

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?

Answer 1

Answer: 400 seconds

Explanation:

5x = 400 + y

4x = y

take 4x and add it to the top so it looks like this:

5x = 400 + 4x

cancel 4x if you don't know how to do it you do it like this you take +4x and instead you do -4x to cancel.

and you do it to 5x so you cancel 4x and 5x - 4x = x so x = 400

x = 400

Answer 2

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:


`d=vt`

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


`D = 400-5t+4t`

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


`0 = 400 - 5t+4t`
∴
`400-t = 0`
∴
`t = 400s`