A and B are typing a 120 page book. A takes 9 hours to type 36 pages, while B takes 5 hours to type 40 pages. A types the first 60 pages alone. The remaining 60 pages are typed by A and B working together. How much total time, in hours, is required to type the complete book?

Introduction / Context:
This problem is a time and work application in the context of typing. It involves two typists with different typing speeds. One person types a portion of the job alone and then both type the remaining pages together. We must compute total time spent to type the entire book.

Given Data / Assumptions:
• Total pages in the book = 120.
• A types 36 pages in 9 hours.
• B types 40 pages in 5 hours.
• A types the first 60 pages alone.
• A and B type the last 60 pages together.
• Typing speeds of A and B remain constant.

Concept / Approach:
We use Work = Rate × Time. First, we determine the typing speed of each person in pages per hour. Then we calculate how much time A takes to type the first 60 pages alone. After that, we determine how long A and B together take to type the remaining 60 pages using their combined speed. Finally, we add both time durations to get the total time.

Step-by-Step Solution:
Typing speed of A = 36 pages ÷ 9 hours = 4 pages per hour. Typing speed of B = 40 pages ÷ 5 hours = 8 pages per hour. First phase: A types 60 pages alone. Time for A to type 60 pages = 60 ÷ 4 = 15 hours. Second phase: A and B type the remaining 60 pages together. Combined typing speed = 4 + 8 = 12 pages per hour. Time to type 60 pages together = 60 ÷ 12 = 5 hours. Total time to type the book = 15 hours + 5 hours = 20 hours.

Verification / Alternative check:
We can check pages produced. In 15 hours, A produces 15 × 4 = 60 pages, which matches the first half of the book. In the next 5 hours, combined output is 5 × 12 = 60 pages, which matches the remaining half. Altogether they produce 120 pages in 20 hours, confirming the correctness of the calculation.

Why Other Options Are Wrong:
Options like 24 hours or 15 hours do not align with the calculated speeds. 24 hours would mean the book is typed at an average speed of just 5 pages per hour, which conflicts with observed rates. Twelve hours is too short, as even A alone needs 15 hours to do his part. Only 20 hours matches both divisions of the work and the combined speed.

Common Pitfalls:
A common mistake is to average the speeds of A and B without considering that they do not work together on the first 60 pages. Another frequent error is to forget that only the last 60 pages are typed jointly, leading to an incorrect total time. Clear separation of the two phases helps avoid such errors.

Final Answer:
The complete book will be typed in 20 hours.