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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: \(y = 12 + \frac{x}{2}\)

Answer :

Answer:

Zeke will catch up with Niko at 16 yards from the start line, y = 16 yards.

Zeke will catch up Niko after 8 seconds, x = 8 seconds.

Step-by-step explanation:

i) distance to be run = 30 yards

ii) Niko has a head start of 12 yards.

iii) speed of Zeke = 2 yards / second

iv) speed of Niko = 1 yard every 2 seconds = 0.5 yard / second

v) x represents the number of seconds they have been racing.

vi) y represents the distance from the start line.

vii) the time at which Zeke catches up with Niko will be given by

[tex]x = \frac{y - 12}{0.5} = \frac{y}{2}[/tex]

Therefore 2y - 24 = 0.5y [tex]\Rightarrow[/tex] 1.5 y = 24 [tex]\therefore[/tex] y = 24 / 1.5 = 16 yards

Therefore x = 16 /2 = 8 seconds

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Rewritten by : Barada

The equations that represent Niko's and Zeke's distance from the start line are [tex]y = 12 + \frac 12 x[/tex] and [tex]y = 2 x[/tex], respectively.

The given parameters are:

[tex]Total = 30[/tex] --- the total distance

Niko is 12 yards ahead, and runs at 1 yard per 2 seconds. So, Niko's equation is

[tex]N i k o = 12 + \frac 12 x[/tex]

Zeke runs 2 yards per seconds. So, Zeke's equation is

[tex]Zeke = 2 x[/tex]

Hence, Niko's and Zeke's distance from the start line are [tex]y = 12 + \frac 12 x[/tex] and [tex]y = 2 x[/tex], respectively.

Read more linear equations at:

https://brainly.com/question/14323743