Question

Joni’s hair is 13 inches long and grows at an average rate of ⅔ in per month. Her friend Kate’s hair is 16 inches long and grows at an average rate of ½ in per month. How many months will pass before the two friends have the same hair length?

Answer 1

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

$Equation : 13 + \frac{2}{3}x ------- eqn\ 1$

Her friend Kate’s hair is 16 inches long and grows at an average rate of ½ in per month

$Equation: 16 + \frac{1}{2}x ----- eqn\ 2$

For two friends to have the same hair length, eqn 1 must be equal to eqn 2

$13 + \frac{2x}{3} = 16 + \frac{x}{2}\\\\\frac{2x}{3} - \frac{x}{2} = 16 - 13\\\\\frac{4x}{6} - \frac{3x}{6} = 3\\\\x = 18$

Thus 18 months will pass before the two friends have the same hair length