Question

When Cai moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 20 inches tall and Tree B was 38 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 3 inches per year. Let A represent the height of Tree A t years after being planted and let B represent the height of Tree B t years after being planted. Write an equation for each situation, in terms of, t, and determine the interval of time, , t, when Tree A is taller than Tree B.

Answer 1

The equation for the height of Tree A, A, t years after being planted is:

A = 20 + 6t

The equation for the height of Tree B, B, t years after being planted is:

B = 38 + 3t

To determine the interval of time when Tree A is taller than Tree B, we can set A greater than B and solve for t:

A > B

20 + 6t > 38 + 3t

Subtracting 3t from both sides:

20 + 3t > 38

Subtracting 20 from both sides:

3t > 18

Dividing both sides by 3:

t > 6

Therefore, Tree A is taller than Tree B when t is greater than 6 years.