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.
