Question

Micah walks on a treadmill at 4 miles per hour. He has walked 2 miles when Luke starts running at 6 miles per hour on the treadmill next to him. If their rates continue, will Luke's distance ever equal Micah's distance? Explain.

Answer 1

Answer:

No

Step-by-step explanation:

they dont go any distance because it is a treadmill

Answer 2

Answer: Yes, at the 1st hour and 6th mile.

Step-by-step explanation:

If $x=$ The number of hours and $y=$ The number of miles, then the system of equations is $\left \{ {{y=4x+2} \atop {y=6x}} \right.$where Micah is the first equation and Luke is the second.

Solve by Substitution:

1) Solve $y=4x+2$ for $y$:

$y=4x+2$

2) Substitute $4x+2$ for $y$ in $y=6x$:

$y=6x$

$4x+2=6x$

3) Add -6x to both sides:

$4x+2+-6x=6x+-6x$

4) Simplify both sides of the equation:

$-2x+2=0$

5) Add -2 to both sides:

$-2x+2+-2=0+-2$

6) Simplify both sides of the equation:

$-2x=-2$

7) Divide both sides by -2:

$\frac{-2x}{-2} =\frac{-2}{-2}$

8) Simplify both sides of the equation:

$x=1$

9) Substitute $1$ for $x$ in $y=4x+2$:

$y=4x+2$

$y=(4)(1)+2$

10) Simplify both sides of the equation:

$y=6$

Therefore, They meet at the 1st hour at the 6th mile

Solve by elimination:

You can't solve the system of equations by elimination

Solve by graphing:

They cross at (1, 6), which supports my answer.