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 + (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 + (1)/(2)x ----- eqn\ 2`

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

`13 + (2x)/(3) = 16 + (x)/(2)\\\\(2x)/(3) - (x)/(2) = 16 - 13\\\\(4x)/(6) - (3x)/(6) = 3\\\\x = 18`

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