Answer:
6 years
Step-by-step explanation:
The shorter tree is 4 ft shorter, but is growing faster. It is making up that difference at the rate of 24-16 = 8 inches = 2/3 ft per year. It will take ...
(4 ft)/(2/3 ft/year) = 4·(3/2) years = 6 years
for the two trees to become the same height.
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If you like, you can write an equation for the height of each tree (in feet or inches) and then solve for the time (t, in years) when the two equations give equal values.
In feet, we have
A height = 8 + (16/12)t
B height = 4 + (24/12)t
These will be equal when ...
8 + (16/12)t = 4 + (24/12)t
4 + (16/12)t = (24/12)t . . . . . . . subtract 4
4 = (8/12)t . . . . . . . . . . . . . . . . .subtract 16/12·t
4·(12/8) = t . . . . . . . . . . . . . . . . multiply by the inverse of the coefficient of t*
6 = t . . . . . . . . . the trees will be the same height in 6 years
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* This is 4·(3/2), which should look very much like the answer we got at the beginning. Note that this is the initial difference in height divided by the difference in growth rates. Multiplying by the inverse of a number is the same as dividing by the number.
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