A blue spruce grows and average of 6 inches per year. A hemlock grows an average of 4 inches per year. If a blue spruce is 4 feet tall and a hemlock is 6 feet tall, when would u expect the trees to be the same height?

1 Answer
Jun 2, 2017

See a solution process below:

Explanation:

The expression for the height of the blue spruce would be:

4 + 1/2y4+12y Where 4 is the starting height in feet and 1/2y12y is how much it grows every year (6 inches = 1/212 foot per year).

The expression for the height of the hemlock would be:

6 + 1/3y6+13yWhere 6 is the starting height in feet and 1/3y13y is how much it grows every year (4 inches = 1/313 foot per year).

We can now equate these two expressions and solve for yy:

4 + 1/2y = 6 + 1/3y4+12y=6+13y

-color(red)(4) + 4 + 1/2y - color(red)(1/3y) = -color(red)(4) + 6 + 1/3y - color(red)(1/3y)4+4+12y13y=4+6+13y13y

0 + 1/2y - color(red)(1/3y) = 2 + 00+12y13y=2+0

1/2y - 1/3y = 212y13y=2

color(red)(6)(1/2y - 1/3y) = color(red)(6) xx 26(12y13y)=6×2

(color(red)(6) xx 1/2y) - (color(red)(6) xx 1/3y) = 12(6×12y)(6×13y)=12

3y - 2y = 123y2y=12

(3 - 2)y = 12(32)y=12

1y = 121y=12

y = 12y=12

It would be expected to take 12 years for both trees to be the same height.