You plant a 4 foot maple tree that grows at a rate of 6 inches per year and a 2 foot birch tree grows at a rate of 8 inches per year . In how many years after planting will the two trees be the same height? How tall will each tree be?
height-maple = (1/2)t + 4
height - birch = (2/3)t + 2
when they have the same height,
(2/3)t + 2 = (1/2)t + 4
times 6, the LCD
4t + 12 = 3t + 24
t = 12
they have the same height 12 years from now
subbing t = 12 into either equation yields
(1/2)12+4 = 10 ft
To find out when the two trees will be the same height, we need to determine how many years it will take for the two trees to reach the same height. Let's call the number of years after planting as 'x'.
The maple tree grows at a rate of 6 inches per year, so after 'x' years, its height would be 4 + 6x feet.
Similarly, the birch tree grows at a rate of 8 inches per year, so after 'x' years, its height would be 2 + 8x feet.
To determine when the two trees will be the same height, we can set up an equation:
4 + 6x = 2 + 8x
Simplifying the equation, we get:
6x - 8x = 2 - 4
-2x = -2
x = 1
So, after 1 year, the maple tree would be 4 + 6(1) = 10 feet tall, and the birch tree would be 2 + 8(1) = 10 feet tall.
Therefore, after 1 year, both trees will be the same height, which will be 10 feet tall.