Adam and Smith are typing a project. Adam takes 6 hours to type 36 pages on a computer, while Smith takes 5 hours to type 40 pages on another computer. If both work together on two different computers, how much time will they take to type a 120-page project?

Introduction / Context:
This question is a time and work problem framed in terms of typing pages. Each person works on a separate computer, so their typing rates add together when they work at the same time. The key is to calculate each person's pages per hour, sum the rates, and then use the combined rate to compute the time required for the given total number of pages.

Given Data / Assumptions:

• Adam types 36 pages in 6 hours.
• Smith types 40 pages in 5 hours.
• Both work simultaneously on separate computers.
• They must type a total of 120 pages.
• Typing speeds remain constant over time.

Concept / Approach:
First, calculate the individual rates in pages per hour. Then, since they are working together on the same project but on different computers, the total rate is the sum of the two rates. Finally, use the formula Time = Total work / Combined rate. Some fraction manipulation is needed to convert the result into hours and minutes for matching with the answer options.

Step-by-Step Solution:
Adam's rate = 36 pages / 6 hours = 6 pages per hour. Smith's rate = 40 pages / 5 hours = 8 pages per hour. Combined typing rate = 6 + 8 = 14 pages per hour. Total work = 120 pages. Time required T = Total work / Combined rate = 120 / 14 hours. Simplify 120 / 14 = 60 / 7 hours. Express 60 / 7 as a mixed number: 60 / 7 = 8 + 4 / 7. Now convert 4 / 7 hours to minutes: 4 / 7 * 60 minutes ≈ 34.2857 minutes. So T ≈ 8 hours and 34 minutes (a bit more than 34 minutes).

Verification / Alternative check:
To verify, convert 8 hours 34 minutes back to hours. 34 minutes is 34 / 60 ≈ 0.5667 hours. Total time ≈ 8.5667 hours. At 14 pages per hour, the total pages typed = 14 * 8.5667 ≈ 119.93 pages, which is very close to 120 pages, the minor difference being due to rounding the minutes. Hence, the nearest precise representation in the options is 8 hours 34 minutes.

Why Other Options Are Wrong:
8 hours corresponds to typing only 14 * 8 = 112 pages. 8 hours 42 minutes is 8.7 hours, which yields 14 * 8.7 = 121.8 pages, more than needed. 8 hours 45 minutes is even longer. Therefore, among the given choices, only 8 hours 34 minutes correctly approximates 60 / 7 hours.

Common Pitfalls:
Many students mis-handle the fractional part 60 / 7 and incorrectly convert it into minutes, or they round too early, leading to an answer that does not match any option. It is better to keep the fraction until the last step and then convert the remainder separately into minutes.

Final Answer:
Working together on two different computers, Adam and Smith will complete the 120-page project in about 8 hours 34 minutes.