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

Accepted Solution

Answer:2.4 yearsStep-by-step 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 inchesType B:4 feet = 4 * 12 = 48 inchesLet "t" be the number of yearsFor Type A, the equation would be:36 + 15t Β [36 inches already and 15 inches per year]For Type B, the equation would be:48 + 10t Β [48 inches and 10 inches per year]Now we equate and solve for "t", the time when both are same height:[tex]36 + 15t = 48 + 10t\\15t-10t=48-36\\5t=12\\t=\frac{12}{5}\\t=2.4[/tex]Hence, after 2.4 years, both trees' heights would be same