Question

A gardener is planting two types of trees. Type A is three feet and grows at a rate of 15 inches per year. Type B is four feet tall and grows at a rate of 10 inches per year. How many years until the trees are the exact same height

Answer 1

2.4 years

Explanation:

We can write two equations for each Type and equate and solve for unknown variable.

First, we need to make the initial height (in ft) to inches.

Type A:

3 feet = 3 * 12 = 36 inches

Type B:

4 feet = 4 * 12 = 48 inches

Let "t" be the number of years

For Type A, the equation would be:

36 + 15t [36 inches already and 15 inches per year]

For Type B, the equation would be:

48 + 10t [48 inches and 10 inches per year]

Now we equate and solve for "t", the time when both are same height:

`36 + 15t = 48 + 10t\\15t-10t=48-36\\5t=12\\t=(12)/(5)\\t=2.4`

Hence, after 2.4 years, both trees' heights would be same