Question

A tree that is 2 feet tall is growing at a rate of 1 foot per year. A 6 -foot tall tree is growing at a rate of

0.5 foot per year. In how many years will the troes be the same height?

Answer 1

It will take 8 years for a tree that is initially 2 feet tall growing at 1 foot per year and a tree that is initially 6 feet tall growing at 0.5 foot per year to reach the same height.

Step-by-step explanation:

The question involves solving for the time when two trees of different initial heights and different growth rates will be the same height. We can set up an equation to represent the growth of each tree. The first tree is 2 feet tall and grows at 1 foot per year, so its height after t years will be 2 feet + 1 foot/year × t. The second tree is 6 feet tall and grows at 0.5 foot per year, so its height after t years will be 6 feet + 0.5 foot/year × t. To find when they will be the same height, we set these two expressions equal to each other:

2 + t = 6 + 0.5t

Now we solve for t:

2 + t = 6 + 0.5t

0.5t = 4

t = 8

So, it will take 8 years for the two trees to be the same height.