a cedar tree is 10 feet tall and grows 12 inches per year. a fir tree is 6 feet tall and grows 18 inches per year. Years until same height?

Question

Is this least common multiple or greatest common factor?

Answer 1

It isn't quite that simple.  This is really two linear equations and you need to find the intersection, but it's pretty easy in this case.

Starting now, the cedar is 10 ft tall and adds 12 inches, or 1 foot,  per year.

That's height, H = 10 + 1y.   (y = years from now.)

The fir is at 6 ft now and adds 1.5 foot per year.

That's H = 6 + 1.5y.

We want to know when they're the same, so just equate the two height expressions and solve for y.

6 + 1.5y = 10 + y

0.5y = 4

y = 8 years.

 

Alternatively, you could do this:

The fir is growing 0.5 foot per year faster and it has (10-6)=4 feet of catching up to do.

y = 4/0.5 = 8