SOLUTION: Will someone please help me with this problem? A tree that is 8 feet tall is growing at a rate of 2 feet each year. Another tree that is 10 feet tall is growing at a rate of 1 foo

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Question 1180346: Will someone please help me with this problem?
A tree that is 8 feet tall is growing at a rate of 2 feet each year. Another tree that is 10 feet tall is growing at a rate of 1 foot each year. Determine how many years it will take for the two trees to reach the same height.

Found 3 solutions by mananth, greenestamps, josgarithmetic:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
let n the numbers of years for both trees to reach same height
tree1
a=8, tn height after n years , d=2
tn = a +(n-1)d
tn= 8 +2n-2
tn =2n+6
Tree 2
tn = 10 +(n-1)1
tn = 9+n
2n+6 = 9+n
n=3

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

Ignore the absurd answer from the other tutor. She blindly used formal mathematics incorrectly to get the wrong answer to a problem that a 3rd grader could answer correctly in a few seconds using informal methods.

3rd grader solution method....
now: tree A 8, tree B 10
in 1 year: tree A 8+2=10, tree B 10+1=11
in 2 years: tree A 10+2=12, tree B 11+1=12
ANSWER: 2 years

Formal algebra....
tree A height after n years: 8+2n
tree B height after n years: 10+1n
8+2n=10+n
n=2

8th-9th grader informal method....
Tree A starts out 2 feet shorter than tree B but each year grows 1 foot more than tree B; the time needed to make up those 2 feet at 1 foot per year is 2 years.

Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website!
x, number of years passing

First Tree

Another Tree

When same height?

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Two years for the two trees each to be 12 feet tall.