Question

Marta and Nicole run laps around the track they run at the same constant speed but Marta starts first when Marta has run 5 laps Nicole has run 3 laps how many laps will Nicole have to run when Marta has run 8 laps

Answer 1

Hello!

The answer is:

Nicole has to run 6 laps when Marta has run 8 laps.

Why?

In order to calculate how many laps will Nicole have to run when Marta has run 8 laps, we need to use two equations.

We must consider that since both Marta's and Nicole's speed are constant all the time, Marta wil always run more laps than Nicole, meaning that there is not possibility for Nicole to run the same number of laps that Marta.

We know that they started at different time at the same constant speed, and when Marta has run 5 laps, Nicole has run 3 laps, there is a difference of 2 laps, and it will be always like that.

So, we can conclude that Marta will always be 2 laps ahead of Nicole.

$Difference=MartaLaps-NicoleLaps\\\\Difference=5Laps-3Laps=2Laps$

For Marta we have:

$MartaLaps=NicoleLaps+2Laps$

For Nicole we have:

$NicoleLaps=MartaLaps-2Laps$

Now, if we want to calculate how many laps will Nicole has to run when Marta has run 8 laps, we need to use the second equation (Nicole's equation) and substitute the number of laps (Marta's lap), so, substituting and calculating we have:

$NicoleLaps=MartaLaps-2Laps$

$NicoleLaps=8Laps-2Laps=6Laps$

Hence, we have that Nicole has to run 6 laps when Marta has run 8 laps.

Have a nice day!