Question

The equation y + 4x = 100 represents your distance y (in meters) from the finish line x seconds after you begin your leg of a relay
race. The equation y + 3.8x= 97 represents your opponent's distance from the finish line. How far do you need to run until you catch
up to your opponent?​

Answer 1

Answer:

  60 m

Step-by-step explanation:

You will catch your opponent when your time and distance (x, y) match those of your opponent. That is, we want to start our solution by finding the (x, y) values that satisfy both equations.

  (y +4x) -(y +3.8x) = (100) -(97)

  0.2x = 3

  x = 15 . . . . . after 15 seconds, both will be the same distance from the finish

Your rate of travel is 4 m/s (the coefficient of x in your distance equation). So, in that 15 seconds it takes to catch your opponent, you will have run ...

  (15 s)(4 m/s) = 60 m

You need to run 60 m to catch your opponent.

_____

You will catch your opponent 40 m from the finish line, which is 60 m from where you started at x=0.