Question

When Cameron moved into a new house, he planted two trees in his backyard. At thetime of planting, Tree A was 24 inches tall and Tree B was 39 inches tall. Each yearthereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. LetA represent the height of Tree At years after being planted and let B represent theheight of Tree B t years after being planted. Write an equation for each situation, interms oft, and determine the interval of time, t, when Tree A is taller than Tree B.

Answer 1

The equations fro each tree will be the inital hight plus the hight they grow so:

`\begin{gathered} A=24+6t \\ B=39+3t \end{gathered}`

Now we need the time when A is bigger than B, so first we are going to find the time when they are equal so A=B

`\begin{gathered} 24+6t=39+3t \\ 6t-3t=39-24 \\ 3t=15 \\ t=(15)/(3)=5 \end{gathered}`

So in 5 years they are going to have the same height, so the solution will be 6 years when A is taller than B

`t>5\text{ years}`