To determine when Edmond and Chase will have completed the same number of lessons, we can establish an equation based on their current progress and the daily completion rates.
-
Edmond's progress:
- Current lessons completed: \( 114 \)
- Lessons completed per day: \( 3 \)
- Total lessons completed after \( x \) days: \( 114 + 3x \)
-
Chase's progress:
- Current lessons completed: \( 122 \)
- Lessons completed per day: \( 2 \)
- Total lessons completed after \( x \) days: \( 122 + 2x \)
We want to find the value of \( x \) where both have completed the same number of lessons:
\[ 114 + 3x = 122 + 2x \]
Now, we will solve for \( x \):
- Subtract \( 2x \) from both sides:
\[ 114 + 3x - 2x = 122 \]
This simplifies to:
\[ 114 + x = 122 \]
- Subtract \( 114 \) from both sides:
\[ x = 122 - 114 \]
This simplifies to:
\[ x = 8 \]
Thus, it will take 8 days for Edmond and Chase to have completed the same number of lessons.
To verify:
-
In 8 days, Edmond will have completed: \[ 114 + 3 \cdot 8 = 114 + 24 = 138 \]
-
In 8 days, Chase will have completed: \[ 122 + 2 \cdot 8 = 122 + 16 = 138 \]
Since both Edmond and Chase will have completed 138 lessons, the solution is confirmed.
The final answer is:
8 days.