Let's assume that both trees will grow to the same height after 't' years.
After 't' years, the height of the first tree (growing at a rate of 1 foot per year) will be 8 + t feet.
Similarly, the height of the second tree (growing at a rate of 1/2 foot per year) will be 10 + (1/2)t feet after 't' years.
If we want both trees to reach the same height, we can set their heights equal to each other and solve for 't':
8 + t = 10 + (1/2)t
Subtracting 8 from both sides, we get:
t = 2 + (1/2)t
Subtracting (1/2)t from both sides, we get:
(1/2)t = 2
Multiplying both sides by 2, we get:
t = 4
Therefore, it will take 4 years for both trees to reach the same height.