Question

Две машинистки вместе могут перепечатать рукопись за 6 часов.После 5 часов совместной работы вторая машинистка продолжила работу самостоятельно и завершила её за 3 часа.За какое время каждая машинистка смогла бы перепечатать рукопись?

Answer 1

Пусть Х - производительность работы 1-ой машинистки
           Y  -  производительность работы 2-ой
6*(X+Y) =5*(X+Y) + 3*Y  - вся работа
6X +6Y =5X+5Y +3Y
X=2Y -->  производительность работы первой в два раза больше второй, то есть за 1 час первая напечатает в 2 раза больше второй.
Вместе они работали 6 часов, первая сделала 2/3 работы, вторая 1/3 всей работы.
6 : 2/3 = 9 час - первая одна выполнит всю работу
6 :1/3 = 18 час вторая выполнит всю работу

Answer 2

Problem Analysis

We are given that two typists can transcribe a manuscript in 6 hours if they work together. After working together for 5 hours, the second typist continues working alone and completes the transcription in 3 hours. We need to determine how long it would take each typist to transcribe the manuscript individually.

Solution

Let's assume that the first typist can transcribe the manuscript in x hours, and the second typist can transcribe it in y hours.

From the given information, we can create the following equation based on the work rates of the typists:

1/x + 1/y = 1/6 ---(1)

We also know that after working together for 5 hours, the second typist completes the transcription in 3 hours. This means that the first typist worked for a total of 5 + 3 = 8 hours.

Using this information, we can create another equation based on the work done by each typist:

(1/x) * 8 + (1/y) * 3 = 1 ---(2)

We now have a system of two equations (1) and (2) that we can solve to find the values of x and y.

Solution Steps

1. Solve equation (1) for y in terms of x: - Multiply both sides of equation (1) by 6xy to eliminate the denominators: 6y + 6x = xy - Rearrange the equation to isolate y: 6y - xy = -6x y(6 - x) = -6x y = -6x / (6 - x)

2. Substitute the value of y in equation (2) with the expression obtained in step 1: (1/x) * 8 + (1/(-6x / (6 - x))) * 3 = 1

3. Simplify equation (2) and solve for x: 8/x - 3(6 - x) / 6x = 1 8/x - (18 - 3x) / 2x = 1 8 - (18 - 3x) / 2 = x 16 - 18 + 3x = 2x x = 2

4. Substitute the value of x back into equation (1) to find y: 1/2 + 1/y = 1/6 1/y = 1/6 - 1/2 1/y = 1/6 - 3/6 1/y = -2/6 y = -6/2 y = -3

Since time cannot be negative, we discard the negative values of x and y. Therefore, the first typist can transcribe the manuscript in 2 hours, and the second typist can transcribe it in 3 hours.

Answer

Each typist would be able to transcribe the manuscript in the following times: - The first typist: 2 hours - The second typist: 3 hours