Two boys write a booklet of 817 lines from opposite ends: Boy 1 from line 1 at 200 lines/h; Boy 2 from line 817 backwards at 150 lines/h. On which line do they meet?

Introduction / Context:
When two agents work from opposite ends toward each other at constant rates, they meet when the cumulative work equals the total. The meeting index corresponds to the work completed by either worker at that instant.

Given Data / Assumptions:

• Total lines = 817.
• Rates: 200 and 150 lines/h.
• They start simultaneously.

Concept / Approach:
Combined rate = 350 lines/h. Meeting time t = total work / combined rate. The line number reached by Boy 1 then is 200t (counting from line 1). Rounding rules imply the first line not yet written by both.

Step-by-Step Solution:
t = 817 / 350 h.Boy 1's line index = 200 * (817/350) = (4/7)*817 ≈ 466.857.They meet between lines 466 and 467, so the meeting line is the 467th.

Verification / Alternative check:
Boy 2 writes 150t ≈ 350.143 lines from the end; 466.857 + 350.143 ≈ 817, consistent.

Why Other Options Are Wrong:
465th or 466th undercount; 468th overshoots the exact balance point.

Common Pitfalls:
Taking arithmetic mean of 1 and 817 rather than using rates; rounding down instead of to the crossing point.

Final Answer:
467th