A young Colorado spruce tree is growing at a rate of 20 cm per year. Currently, it is 244 cm tall. A 300 cm tall white spruce tree is growing at a rate of 12 m per year. In how many years will the two trees be the same height? Solve algebraically
After n years,
244+20n = 300+12n
8n = 56
n=7
So, in 7 years they will both be 384 cm tall
To solve this problem algebraically, we'll set up an equation and solve for the number of years it takes for the two trees to be the same height.
Let's call the number of years it takes for the trees to be the same height "x".
The height of the young Colorado spruce tree is given by the equation:
Height = Growth rate * Number of years + Initial height
So for the young Colorado spruce tree, the equation is:
244 = 20x + Initial height
The height of the white spruce tree is given by the equation:
Height = Growth rate * Number of years + Initial height
So for the white spruce tree, the equation is:
300 = 12x + Initial height
Now, we need to find the initial height for both trees. The initial height is the height at time 0. From the information given, it is not specified. We can assume it to be 0 for simplicity.
Using this assumption, the equations become:
244 = 20x + 0
300 = 12x + 0
Simplifying the equations, we have:
244 = 20x
300 = 12x
To solve for x, we can divide both sides of each equation by their respective growth rates:
244/20 = 20x/20
300/12 = 12x/12
This gives us:
12.2 = x
25 = x
Therefore, it will take approximately 12.2 years or 25 years for the two trees to be the same height.
Note: In this problem, we made the assumption that the initial heights of both trees are 0. It's important to note that in real-life scenarios, the initial heights may not be zero, so this assumption may not be accurate.