Question

Первая машинистка может перепечатать рукопись за 20 ч, а вторая за 30ч. Обе работали вместе 10 ч затем 3 ч работала только вторая. Третья машинистка закончила работу за 1 ч. За сколько часов может перепечатать рукопись третья машинистка?

Answer 1

1 машинистка может перепечатать рукопись за 20 ч.
За 10 ч она перепечатала 1/2 рукописи.
2 машинистка может перепечатать рукопись за 30 ч.
За 10 ч она перепечатала 1/3 рукописи, а за 3 часа 1/10 рукописи.
Вместе они за 10 ч перепечатали 1/2 + 1/3 = 5/6 = 50/60 рукописи.
Потом вторая за 3 часа перепечатала 1/10 = 6/60 рукописи.
Всего они вдвоем напечатали 50/60 + 6/60 = 56/60 = 14/15 рукописи.
Третья машинистка напечатала последние 1/15 рукописи за 1 час.
Всю рукопись третья машинистка перепечатает за 15 часов.

Answer 2

Problem Analysis

We are given that the first typist can transcribe a manuscript in 20 hours, the second typist can transcribe it in 30 hours, and both of them worked together for 10 hours. After that, only the second typist worked for 3 hours, and finally, the third typist finished the work in 1 hour. We need to determine how long it would take for the third typist to transcribe the manuscript.

Solution

To solve this problem, we can calculate the combined work rate of the first and second typists and then use that to find the work rate of the third typist. Let's break down the problem step by step:

1. Calculate the combined work rate of the first and second typists: - The first typist can transcribe the manuscript in 20 hours, so their work rate is 1/20 manuscripts per hour. - The second typist can transcribe the manuscript in 30 hours, so their work rate is 1/30 manuscripts per hour. - When they work together, their combined work rate is the sum of their individual work rates: 1/20 + 1/30 = 1/12 manuscripts per hour.

2. Calculate the total work done by the first and second typists in the 10 hours they worked together: - Their combined work rate is 1/12 manuscripts per hour. - In 10 hours, they would have transcribed 10 * (1/12) = 5/6 of the manuscript.

3. Calculate the work done by the second typist in the 3 hours they worked alone: - The second typist's work rate is 1/30 manuscripts per hour. - In 3 hours, they would have transcribed 3 * (1/30) = 1/10 of the manuscript.

4. Calculate the remaining work that needs to be done by the third typist: - The total work done by the first and second typists is 5/6 of the manuscript. - The work done by the second typist alone is 1/10 of the manuscript. - So, the remaining work is 1 - (5/6 + 1/10) = 1 - (25/30 + 3/30) = 1 - (28/30) = 2/30 = 1/15 of the manuscript.

5. Calculate the work rate of the third typist: - The third typist can transcribe the remaining 1/15 of the manuscript in 1 hour. - So, their work rate is 1/15 manuscripts per hour.

6. Calculate the time it would take for the third typist to transcribe the entire manuscript: - The third typist's work rate is 1/15 manuscripts per hour. - So, it would take them 15 hours to transcribe the entire manuscript.

Therefore, the third typist can transcribe the manuscript in 15 hours.

Answer

The third typist can transcribe the manuscript in 15 hours.