Final answer:
To find how long it takes two computers to send all the company's emails when working together, calculate the sum of their individual work rates (1/60 and 1/40), which is 5/120 tasks per minute, and take the reciprocal to get the combined time, resulting in 24 minutes.
Step-by-step explanation:
The problem involves calculating the combined work rate of two computers completing the same task. As such, the problem can be solved using the concept of work rates in mathematics. If the slower computer can complete the task in 60 minutes and the faster computer in 40 minutes, we need to determine their combined rate of work when they function simultaneously.
First, we express the work rates of both computers as fractions of the task completed per minute: the slower computer's rate is 1/60 tasks per minute and the faster computer's rate is 1/40 tasks per minute. When these two rates are added together, we get the combined rate:
Combined Rate = (1/60 + 1/40) tasks per minute
To solve this, we need a common denominator, which in this case is 120. So we rewrite the rates:
Combined Rate = (2/120 + 3/120) tasks per minute = 5/120 tasks per minute
To find the time it takes to complete the task working together, we take the reciprocal of the combined rate:
Time = 1 / (5/120) minutes = 120/5 minutes = 24 minutes
Therefore, it would take both computers working together 24 minutes to send all of the company's emails.