Wyatt receives a plant that is 7 cm tall. It grows another 2 cm each month. Harper receives a seed, so the plant initially has no height, and it grows at a rate of 3 cm each month. Will the plants ever be the same height at the same time? If so, when will that happen?

Question

How tall is each plant initially?
Wyatt’s plant is initially
cm tall and Harper’s plant is initially
cm tall.

Answer 1

Wyatt's plant is initially 7 cm tall, and Harper's plant is initially 0 cm tall (since it is a seed).

To determine if and when the two plants will be the same height, we can set up a mathematical equation based on the growth rates:

Let \( t \) be the number of months after they start growing.

• The height of Wyatt's plant after \( t \) months is: \[ H_W = 7 + 2t \]

• The height of Harper's plant after \( t \) months is: \[ H_H = 0 + 3t = 3t \]

We want to find out when these two heights are equal: \[ 7 + 2t = 3t \]

Now, we solve for \( t \): \[ 7 = 3t - 2t \] \[ 7 = t \]

So, after 7 months, both plants will be the same height.

To check the heights at \( t = 7 \):

• Wyatt's plant height: \[ H_W = 7 + 2(7) = 7 + 14 = 21 \text{ cm} \]

• Harper's plant height: \[ H_H = 3(7) = 21 \text{ cm} \]

Thus, both plants will be 21 cm tall after 7 months.

In summary:

• Wyatt’s plant is initially 7 cm tall.
• Harper’s plant is initially 0 cm tall.
• The plants will be the same height after 7 months.