Question

There are three typists in an office. Each typist can type an average of 6 letters per hour. If letters arrive for being typed at the rate of 15 letters per hour, what fraction of the time all the typists will be busy?

(a) 2/5
(b) 3/5
(c) 4/5
(d) 1/2

Answer 1

The fraction of time all typists will be busy is 5/6, which is calculated by dividing the arrival rate of letters by the total typing capacity of the typists. However, this answer is not listed among the provided options, indicating a possible error in the question.

Step-by-step explanation:

The question asks us to find the fraction of time all typists in an office will be busy given that each typist can type an average of 6 letters per hour and letters arrive to be typed at the rate of 15 letters per hour. There are three typists, so the combined typing rate for all typists is 3 typists × 6 letters per typist per hour = 18 letters per hour. Since 15 letters arrive each hour, and the typists can collectively type 18 letters per hour, they have more than enough capacity to handle the incoming letters.

To calculate the fraction of time all typists will be busy, we divide the rate at which letters arrive by the total rate at which letters can be typed by all typists. This gives us 15 letters per hour ÷ 18 letters per hour = 5/6. The fraction of time all typists will be busy is 5/6, which is not an option among the given choices (a) 2/5 (b) 3/5 (c) 4/5 (d) 1/2. Therefore, it seems there might be an error in the available options.