Question

Два наборщика ,работая вместе,напечатают рукопись за 5 часов.если первый наборщик будет работать один 6 часов,то второму потребуется 3 часа,чтобы закончить работу.за сколько часов второй наборщик выполнит всю работу один?

Answer 1

1-ый за 1 час -- Х работа/час - производительность труда
2-ой за 1 час -- Y работа/час
Вместе за пять часов: 5*(X+Y) - вся работа, сделанная совместно.
(6*X+3*Y)  - вся работа, сделанная первым и продолжена вторым:
Это одна и та же работа:
5*(X+Y)=(6*X+3*Y) 
5X + 5Y = 6X+3Y
X= 2Y,  т.е. у первого производительность больше, чем у второго, в 2 раза.
то есть 1-ый выполнит 2 части работы, а второй -1 часть работы за 1 час, 
для второго понадобится в два раза больше времени для выполнения работы, которую выполнил 1-ый, 6 *2=12. и: 12+3=15 (часов), чтобы второй один выполнил всю работу.   
  

Answer 2

Problem Analysis

We are given that two typists working together can complete a manuscript in 5 hours. If the first typist works alone for 6 hours, the second typist will take 3 hours to complete the remaining work. We need to determine how long it will take for the second typist to complete the entire work alone.

Solution

Let's assume that the first typist's work rate is represented by x and the second typist's work rate is represented by y.

From the given information, we can set up the following equations:

1. The combined work rate of the two typists is equal to the reciprocal of the time taken to complete the work together: - (1/x + 1/y) = 1/5 2. If the first typist works alone for 6 hours, the second typist will take 3 hours to complete the remaining work: - (1/x) * 6 + (1/y) * 3 = 1 To solve these equations, we can use substitution or elimination methods. Let's use the substitution method:

From equation 2, we can express (1/x) in terms of (1/y): - (1/x) = 1 - (1/y) * 3/6 - (1/x) = 1 - (1/y) * 1/2 - (1/x) = (2 - 1/y) / 2

Substituting this value of (1/x) into equation 1, we get: - ((2 - 1/y) / 2 + 1/y) = 1/5 - (2 - 1/y + 2/y) / 2 = 1/5 - (2 + 1/y) / 2 = 1/5 - 2 + 1/y = 2/5 - 1/y = 2/5 - 2 - 1/y = -8/5 - y = -5/8

Since the work rate cannot be negative, we can conclude that the second typist's work rate is 5/8.

Now, let's find the time it will take for the second typist to complete the entire work alone. We can use the formula Time = Work / Rate.

The work is equal to 1 (the entire manuscript), and the rate is 5/8 (the second typist's work rate).

- Time = 1 / (5/8) - Time = 8/5

Therefore, it will take the second typist 8/5 hours to complete the entire work alone.

Answer

The second typist will take 8/5 hours to complete the entire work alone.

Explanation

When the first typist works alone for 6 hours, they complete 1/6 of the work. The remaining work is 1 - 1/6 = 5/6.

Since the second typist takes 3 hours to complete the remaining work, their work rate can be calculated as follows: - Work Rate = Work / Time - Work Rate = (5/6) / 3 - Work Rate = 5/18

Therefore, the second typist's work rate is 5/18.

To find the time it will take for the second typist to complete the entire work alone, we can use the formula Time = Work / Rate: - Time = 1 / (5/18) - Time = 18/5 - Time = 3.6 hours

Therefore, the second typist will take approximately 3.6 hours to complete the entire work alone.

Note

It's important to note that the given problem assumes a linear relationship between work rate and time. This means that the work rate remains constant throughout the entire duration of work. In real-life scenarios, work rates may vary due to factors such as fatigue or breaks.