Respuesta :
9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.
Step-by-step explanation:
The given is,
        Type A is 10 feet tall and grows at a rate of 21 inches per year
        Type B is 7 feet tall and grows at a rate of 25 inches per year
Step:1
       Convert the rate of grows of tree inch to feet,
       For Tree A,
          Rate of grow, A = 21 inches per year
                       = 21 × 0.0833333    ( 1 inch = 0.0833333 feet)
                       = 1.75 feet per year
       For Tree B,
          Rate of grow, B = 25 inches per year
                       = 25 × 0.0833333   ( 1 inch = 0.0833333 feet)
                       = 2.08333 feet per year
Step:2
      Difference in the tall of  Tree A & B,
                        = 10 - 7
                       = 3 feet
      Difference in the rate of grow of tree A & B,
                        = 2.08333 - 1.75
                        = 0.3333325 feet per year
Step:3
      Year take to both trees are same height,
                        [tex]= \frac{Difference in the height of tree A & B}{Difference in the rate of grows of A & B}[/tex]
                        [tex]= \frac{3}{0.3333325}[/tex]
                        [tex]= 9.00[/tex]
                        = 9 years
Step:4
      Check for solution,
      Height of tree = Height of Tree + (Rate of grow × Years)
      For A,
                  = 10 + ( 1.75 × 9 )
                  = 25.75 feet.........................................(1)
      For B,
                  = 7 + ( 2.08333 × 9 )
                  = 25.74999
                  ≅ 25.75 feet.....................................(2)
     From Equation (1) and (2),
         25.75 feet = 25.75 feet
Result:
     9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.
