18 months will pass before the two friends have the same hair length
Solution:
Let "x" be the number of months
Joni’s hair is 13 inches long and grows at an average rate of ⅔ in per month
[tex]Equation : 13 + \frac{2}{3}x ------- eqn\ 1[/tex]
Her friend Kate’s hair is 16 inches long and grows at an average rate of ½ in per month
[tex]Equation: 16 + \frac{1}{2}x ----- eqn\ 2[/tex]
For two friends to have the same hair length, eqn 1 must be equal to eqn 2
[tex]13 + \frac{2x}{3} = 16 + \frac{x}{2}\\\\\frac{2x}{3} - \frac{x}{2} = 16 - 13\\\\\frac{4x}{6} - \frac{3x}{6} = 3\\\\x = 18[/tex]
Thus 18 months will pass before the two friends have the same hair length
