Question

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

Answer 1

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

     $x = \frac{y - 12}{0.5} = \frac{y}{2}$

    Therefore 2y - 24 = 0.5y     $\Rightarrow$  1.5 y = 24    $\therefore$ y = 24 / 1.5  = 16 yards

Therefore x  = 16 /2  = 8 seconds

Answer 2

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

The given parameters are:

$Total = 30$ --- the total distance

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

$N i k o = 12 + \frac 12 x$

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

$Zeke = 2 x$

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

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