Respuesta :
Given:
Your distance y (in meters) from the finish line x seconds after you begin your leg of a relay race is
[tex]y+4x=100[/tex]
Opponent's distance is
[tex]y+3.7x+94[/tex]
To find:
The distance you need to run to catch up with your opponent.
Solution:
We have,
[tex]y+4x=100[/tex] ...(i)
[tex]y+3.7x+94[/tex] ...(ii)
Subtract (ii) from (i), we get
[tex]y+4x-y-3.7x=100-94[/tex]
[tex]0.3x=6[/tex]
Divide both sides by 0.3.
[tex]x=\dfrac{6}{0.3}[/tex]
[tex]x=20[/tex]
Put x=20 in (i).
[tex]y+4(20)=100[/tex]
[tex]y+80=100[/tex]
[tex]y=100-80[/tex]
[tex]y=20[/tex]
They will meet at (20,20). It means at 20 meters from the finish line after 20 seconds from the beginning.
Put x=0 in (i), we get
[tex]y+4(0)=100[/tex]
[tex]y=100[/tex]
It means, initially the total distance you and finish line is 100 meters.
You will catch your opponent 20 meter from the finish line. So,
[tex]100-20=80[/tex]
Therefore, you need to run 80 meters to catch up with your opponent.
