Question

A botanist is studying the growth rates of live oaks. He wants to know the rates at which the height and circumference increase. He knows that the height typically increases 16 times as fast as the circumference. He measures a 10-year-old live oak and finds that: height + circumference = 255in. What is the oak's rate of growth of height and circumference? (Hint: Set up two equations in two variables and solve the system.)

Answer 1

say there are "x" county residents and "y" non. x+y = 11 and 8x+10y = 96
x = 11-y
8 (11-y) +10y = 96
88 - 8y +10y = 96
88 +2y = 96
2y = 8
y = 4
x = 7

Let's say she climbed "L" minutes on the lower and "U" minutes on the upper

1.2 *L = distance of the lower
.8*U = distance of the upper
L+U = 51.5 min.

Unfortuantly we're not given the total height of the wall, or how the halves relate to each other (equal distance? equal time?) I don't believe you're given enough information to solve this....

if m = years to maturity and a = current age

900m + 2200(a-m) = 2,900,000

and once again we're not given enough information to proceed... we need the current age of the tree to solve

if "h" = rate height changes and "c" = rate circumference changes, both in inches/yr
h = 16c
10h = height growth in 10 yrs
10c = circumference growth in 10 yrs
10h + 10c = 255

10(16c) +10c =255
160c+10c = 255
170c = 255
c = 1.5 in/yr
h = 24 in/yr