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.



How many days before the plants are the same height?

Answer 1

To find out how many days it will take for the two bamboo plants to be the same height, we can set up equations for the height of each plant over time.

Let \( d \) be the number of days from now.

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

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

We want to find \( d \) such that the heights are equal:
\[
6 + 4d = 10 + 2d
\]

Now, let's solve for \( d \):

1. Subtract \( 2d \) from both sides:
\[
6 + 2d = 10
\]

2. Subtract 6 from both sides:
\[
2d = 4
\]

3. Divide both sides by 2:
\[
d = 2
\]

Thus, it will take **2 days** for the plants to be the same height.

Now, let's verify this:
- After 2 days, the height of Plant A will be:
\[
6 + 4(2) = 6 + 8 = 14 \text{ inches}
\]
- After 2 days, the height of Plant B will be:
\[
10 + 2(2) = 10 + 4 = 14 \text{ inches}
\]

Indeed, both plants will be 14 inches tall after 2 days, confirming our solution.