Question

A gardener is planting two types of trees: type a is 3 feet tall and grows at a rate of 16 inches per year. type b is 4 feet tall and grows at a rate of 13 inches per year. algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

So you have 2 trees. One grows at 16 inches per year and is 3 feet tall while the other grows 13 inches tall and is 4 feet tall. 
First, lets make some equations for the trees. 
Tree a- y=16x+36
Tree b- y=13x+48
If you use a graphing calculator, and input the equations you can see that the 2 lines meet up at (4,100)
Which means that after 4 years they will be the same height.