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 4 solutions by mananth, greenestamps, josgarithmetic, ikleyn:
Answer by mananth(16949)   (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(13287)  (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(39713)  (Show Source):
Answer by ikleyn(53541)  (Show Source):
You can put this solution on YOUR website! .
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.
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@mananth gives the answer 3 years.
But if you check it, you will see that first tree will be 8 + 3*2 = 14 m tall,
while the second tree will be 10 + 3 = 13 m tall in 3 years.
So, the solution and the answer by @mananth both are INCORRECT.
I came to bring a correct solution.
The correct formula for the first tree height is
h1(t) = 8 + 2t, where t is the time in years from now, in years.
For the first tree height is
h2(t) = 10 + t, where t is the time in years from now, in years.
We equate two heights
8 + 2t = 10 + t,
2t - t = 10 - 8,
t = 2.
ANSWER. Two trees will reach the same height in 2 years from now.
Solved correctly.
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