Question

my teacher was teaching us this earlier but she didn't actually explain because she focuses on the class but I'm on virtual it said something went wrong with the other tutor

Answer 1

We have that Liam runs 4 miles per hour and gets a 0.25 mile head start. We can write the relation function of this event like this:

`y=4x+0.25`

Now, Harper runs 0.5 miles per hour faster than Liam. We can represent this in the following way:

`\begin{gathered} \text{Harper's speed = Liam's speed + 0.5m/h}=4+0.5=4.5m/h \\ \end{gathered}`

then, the relation function for Harper is:

`y=4.5x`

Since Liam and Harper run the same distance, we can match both equations to get the following expression:

`4x+0.25=4.5x`

to find how many hours do they run, we have to solve for x:

`\begin{gathered} 4x+0.25=4.5x \\ \Rightarrow0.25=4.5x-4x \\ \Rightarrow0.25=0.5x \\ \Rightarrow x=(0.25)/(0.5)=0.5 \\ x=0.5 \end{gathered}`

we have that x = 0.5, this means that they both run for half and hour the same distance.