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?

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Answer 1 · 2017-06-02T19:26:14

See a solution process below:

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

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

The expression for the height of the hemlock would be:

#6 + 1/3y#Where 6 is the starting height in feet and #1/3y# is how much it grows every year (4 inches = #1/3# foot per year).

We can now equate these two expressions and solve for #y#:

#4 + 1/2y = 6 + 1/3y#

#-color(red)(4) + 4 + 1/2y - color(red)(1/3y) = -color(red)(4) + 6 + 1/3y - color(red)(1/3y)#

#0 + 1/2y - color(red)(1/3y) = 2 + 0#

#1/2y - 1/3y = 2#

#color(red)(6)(1/2y - 1/3y) = color(red)(6) xx 2#

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

#3y - 2y = 12#

#(3 - 2)y = 12#

#1y = 12#

#y = 12#

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