Question

A gardener is planting two types of trees: Type A is 3 feet tall and grows at a rate of 18 inches per year. Type B is 4 feet tall and grows at a rate of 10 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

Answer 1

x = 1.5 years

Explanation:

3 feet = 3·12 inches

3·12 + 18·x = 4·12 + 10·x

36 + 18·x = 48 + 10·x

36 + 8·x = 48

8·x = 12

x = 12/8 = 1.5 years

Answer 2

Both type of trees will be of equal height after 1.5 years.

Explanation:

Let both type (type A and type B) of trees will be of exactly same height after x years.

Type A trees are 3 feet or 36 inches tall and growing at the rate of 18 inches per year.

So the height of type A trees after x years will be = (18x + 36) inches.

Type B trees are 4 feet or 48 inches tall and growing at a rate = 10 inches per year

The height of type B trees after x years = (10x + 48) inches

Since after x years both type of trees are of the same height

Therefore, (18x + 36) = (10x + 48)

18x - 10x = 48 - 36

8x = 12

x =
`(12)/(8)`

x = 1.5 years