When Rahul moved into a new house, he planted two trees in his backyard. At the time of planting, Tree A was 32 inches tall and Tree B was 20 inches tall. Each year thereafter, Tree A grew by 6 inches per year and Tree B grew by 9 inches per year. Let AA represent the height of Tree A tt years after being planted and let BB represent the height of Tree B tt years after being planted. Write an equation for each situation, in terms of t, commat, and determine the number of years after the trees were planted when both trees have an equal height.
Answer
Attempt 1 out of 4
A, equalsA=
B, equalsB=
Answer:
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AA represents the height of Tree A in inches t years after being planted:
AA = 32 + 6t
BB represents the height of Tree B in inches t years after being planted:
BB = 20 + 9t
To determine the number of years after the trees were planted when both trees have an equal height, we need to set AA equal to BB and solve for t:
32 + 6t = 20 + 9t
Simplifying the equation:
32 - 20 = 9t - 6t
12 = 3t
t = 4
Therefore, after 4 years, both trees will have an equal height.