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Mandy is skating at 5 miles per hour. Nikki is skating at 6 miles per hour and started 1 mile behind Mandy. If their rates stay the same, will Mandy catch up with Nikki? Explain.

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Answer: Yes

Step-by-step explanation:

The system of equations would be [tex]\left \{ {{5t=6t-1} \atop {6t-1=5t}} \right.[/tex]

Solve by substitution:

1) Add [tex]1[/tex] to both sides of the equation:

[tex]6t -1+ 1 = 5t + 1[/tex]

2) Simplify:

[tex]6t=5t+1[/tex]

3) Subtract [tex]5t[/tex] to both sides of the equation:

[tex]6t - 5t = 5t -5t + 1[/tex]

4) Simplify:

[tex]t=1[/tex]

When they have skated for [tex]1[/tex] hour, Mandy will catch up to Nikki.

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