A gardener is planting two types of trees: Type A is 3 feet tall and grows at a rate of 23 inches per year. Type B is 6 feet tall and grows at a rate of 17 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer: it will take 0.5 year for these trees to be the same height.

Step-by-step explanation:

Let x represent the number of years it will take for these trees to be the same height.

Type A is 3 feet tall and grows at a rate of 23 inches per year. It means that the height of Type A after x years is

23x + 3

Type B is 6 feet tall and grows at a rate of 17 inches per year. It means that the height of Type B after x years is

17x + 6

For the height of both trees to be the same, the number of years would be

23x + 3 = 17x + 6

23x - 17x = 6 - 3

6x = 3

x = 3/6

x = 0.5