Question

The relationship between time in months, t, and height in cm, h, can be represented by the equation h=4+2t for Plant A and h=8+t for Plant B.
Solve the equation below to find the value of t, or the time in months when the heights of Plant A and Plant B are equal.
h=4+2t
h=8+t

Height of Plant A
=
Height of Plant B
Plant A: y=2x+4
Plant B: y=x+8

2x+4=x+8
4+2t
=
8+t

t
=

Answer 1

To find the time in months \( t \) when the heights of Plant A and Plant B are equal, we will set their height equations equal to each other and solve for \( t \).

The equations for the heights are:
1. Plant A: \( h = 4 + 2t \)
2. Plant B: \( h = 8 + t \)

Setting the equations equal to each other:

\[
4 + 2t = 8 + t
\]

Now, we will solve for \( t \):

1. Subtract \( t \) from both sides:

\[
4 + 2t - t = 8
\]

This simplifies to:

\[
4 + t = 8
\]

2. Now, subtract 4 from both sides:

\[
t = 8 - 4
\]

This gives:

\[
t = 4
\]

Thus, the time in months when the heights of Plant A and Plant B are equal is \( t = 4 \).