zeke is racing his little brother

Zeke is racing his little brother Niko. They are running a total of 30 yards, and Zeke gives Niko a 12-yard head start. Zeke runs 2 yards every second, but Niko only runs 1 yard every 2 seconds. If $x$ represents the number of seconds they have been racing, and $y$ represents the distance from the start line, then:

• For Zeke: $y=2x$
• For Niko: $y=12+\frac{x}{2}$

Zeke and Niko are racing a total of 30 yards. Zeke gives Niko a 12-yard head start. Zeke runs 2 yards per second, while Niko runs 1 yard every 2 seconds.

Explanation:
To represent the positions of Zeke and Niko over time:

• Zeke’s position after x seconds is given by the equation: $y = 2x$, since he runs 2 yards per second.

• Niko’s position after x seconds is given by: $y = 12 + \frac{x}{2}$, since he starts 12 yards ahead and runs 1 yard every 2 seconds.

Answer:
After finding the value of x when their positions are the same, we solve the equation $2x = 12 + \frac{x}{2}$.