Question

You are 36 miles from a friend. You both start riding your bikes toward each other at the same time. You travel 15 miles per hour and your friend travels 3 miles slower. How far will you travel before you meet your friend?

Answer 1

I wil have traveled 20 miles by the moment I meet my friend

Explanation:

Hi

We are going to use de following formula
`x_(f)=vt+x_(0)`

In my case speed will be positive, so
`v=15mi/h` and
`x_(0)=0mi`, For my friend speed will be negative, so
`v=-12mi/h` and
`x_(0)=36mi`. Then we can build two equations

(1)
`x_(f)=15t+0 \ or \ t=(x_(f))/(15)`

(2)
`x_(f)=-12t+36`

By replacing (1) in (2)
`x_(f)=-12((x_(f))/(15) )+36=-(4)/(5) x_(f)+36`

Multiplying both sides by 5

`5x_(f)=-4x_(f)+180\\9x_(f)=180\\x_(f)=(180)/(9) =20`

So I wil have traveled 20 miles by the moment I meet my friend.