Question

You plant a 4 foot maple tree that grows at a rate of 6 inches per year and a 2 foot birch tree grows at a rate of 8 inches per year . In how many years after planting will the two trees be the same height? How tall will each tree be?

Answer 1

height-maple = (1/2)t + 4
height - birch = (2/3)t + 2

when they have the same height,
(2/3)t + 2 = (1/2)t + 4
times 6, the LCD
4t + 12 = 3t + 24
t = 12

they have the same height 12 years from now
subbing t = 12 into either equation yields
(1/2)12+4 = 10 ft