Patrick W. answered • 12/18/14

High School Mathematics Teacher, Passionate Math Geek

ok, I'm reading that the tree has grown to 40½ feet in 7½ years, is that correct?

If so, I'm guessing the second part of the question is how long until the tree is 57 feet tall.

Well let's break that down a bit. As a separate example, if a 2 year old tree was four feet tall, then we could say that its rate of growth was 4 feet in 2 years, or 4/2 feet per year, but 4/2=2. So actually, we could say that this tree grows 2 feet per year.

With your example, the numbers are a bit trickier but we should be able to do the same thing. If a 7½ year old tree is 40½ feet tall, then we could say that its rate of growth is 40.5/7.5. We can try to simplify this, or we can use a calculator to see that 40.5/7.5 = 5.4 feet per year.

So if our tree grows 5.4 feet per year, we still have to figure out how long it will take to reach 57 feet. Well we don't know how long it will take, so let's call the number of years it would take "x". How many years does it take to reach 57 feet tall? x years. That means we could say that the trees rate of growth is 57/x feet per year, but we already said that this rate is 5.4. That means they must be the same rate, so 5.4=57/x

With some algebra on this equation, we can find

5.4=57/x

5.4x=57

x=57/5.4

x=10.55

It would take 10.55 years for this tree to reach 57 feet high

Does that answer your questions?