Question

Suppose you are testing 2 fertilizers on bamboo plants A and B which are growing under identical conditions. Plant A is 6 inches tall and growing at a rate of 4 inches each day. Plant B is 10 inches and growing at a rate of 2 inches each day.



What height will the plants be when they are the same?

Answer 1

To find out when the heights of Plant A and Plant B will be the same, we can set up equations for the height of each plant over time.

Let \( t \) represent the number of days of growth.

The height of Plant A after \( t \) days can be expressed as:
\[
\text{Height of Plant A} = 6 + 4t
\]

The height of Plant B after \( t \) days can be expressed as:
\[
\text{Height of Plant B} = 10 + 2t
\]

To find out when the heights are the same, we can set the two equations equal to each other:
\[
6 + 4t = 10 + 2t
\]

Next, we'll solve for \( t \):
1. Subtract \( 2t \) from both sides:
\[
6 + 2t = 10
\]
2. Subtract 6 from both sides:
\[
2t = 4
\]
3. Divide both sides by 2:
\[
t = 2
\]

Now that we have \( t = 2 \), we can substitute back to find the height of both plants at this time:

For Plant A:
\[
\text{Height of Plant A} = 6 + 4(2) = 6 + 8 = 14 \text{ inches}
\]

For Plant B:
\[
\text{Height of Plant B} = 10 + 2(2) = 10 + 4 = 14 \text{ inches}
\]

Thus, both plants will be 14 inches tall when they are the same height.