Edmond and Chase are both enrolled in an online foreign-language program. Edmond has already completed 114 lessons, and he will be completing 3 more lessons each day. Chase has already completed 122 lessons, and he will be completing 2 more lessons each day.

Question

How long will it take for Edmond and Chase to have completed the same number of lessons?

Answer 1

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.

1. Edmond's progress:

   • Current lessons completed: \( 114 \)
   • Lessons completed per day: \( 3 \)
   • Total lessons completed after \( x \) days: \( 114 + 3x \)

2. 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 \( x \):

1. Subtract \( 2x \) from both sides:

\[ 114 + 3x - 2x = 122 \]

This simplifies to:

\[ 114 + x = 122 \]

2. 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.