Let's continue solving the equation step by step.
Starting from where we left off:
We had:
\[ 20 + 2x = 30 - 20 \]
This simplifies to:
\[ 20 + 2x = 10 \]
Now, to isolate \( 2x \), we subtract 20 from both sides:
\[ 2x = 10 - 20 \]
This gives us:
\[ 2x = -10 \]
Next, to find \( x \), we will divide both sides by 2:
\[ x = \frac{-10}{2} \]
This simplifies to:
\[ x = -5 \]
However, it seems there was an error in the previous calculation. Let’s check our work and ensure we kept our moves correct.
Let's revisit the subtraction of \( 20 \) from both sides:
Actually, from
\[ 20 + 2x = 30 \]
If we subtract 20 from both sides, we have:
\[ 2x = 30 - 20 \]
This indeed gives:
\[ 2x = 10 \]
Now, if we divide both sides by 2:
\[ x = \frac{10}{2} \]
This simplifies correctly to:
\[ x = 5 \]
So, \( x = 5 \) weeks is indeed correct!
Now, to confirm the values when \( x = 5 \):
For Steven:
- Miles = \( 20 + 4(5) = 20 + 20 = 40 \)
For Irene:
- Miles = \( 30 + 2(5) = 30 + 10 = 40 \)
Both Steven and Irene run the same distance of 40 miles after 5 weeks.
Thus, the point of intersection is \( (5, 40) \).