Question

Ребята помогите плиииз!!!!Двое рабочих,работая вместе,могут выполнить некоторую работу за 4 дня.Если треть работы выполнит первый рабочий,а затем его сменит второй,то все задание будет выполненно за 10 дней.За сколько дней может выполнить эту работу каждый рабочий,работая самостоятельно.

Answer 1

х- в день 1,у-в день 2
1/(х+у)=4⇒х+у=1/4⇒у=1/4-х
1/3х+2/3у=10⇒у+2х=30ху
1/4-х+2х=30х(1/4-х)
0,25+х-7,5х+30х²=0
30х²-6,5х+0,25=0
D=42,25-30=12,25    √D=3,5
x1=(6,5-3,5)/60=3/60=1/20⇒y1=1/4-1/20=4/20=1/5
x2=(6,5+3,5)/60=10/60=1/6⇒y2=1/4-1/6=1/12
1)x1=1/20⇒1:1/20=20дней
у1=1/5⇒1:1/5=5дней
2)х2=1/6⇒1:1/6=6дней
у2=1/12⇒1:1/12=12дней

Answer 2

Problem Analysis

We have two workers who can complete a certain task in 4 days when working together. If the first worker completes one-third of the task and then is replaced by the second worker, the entire task is completed in 10 days. We need to determine how many days each worker would take to complete the task individually.

Solution

Let's assume that the total work is represented by the variable "W".

According to the given information, when the two workers work together, they can complete the task in 4 days. This means that their combined work rate is 1/4 of the total work per day.

When the first worker completes one-third of the task, the remaining work is (2/3)W. The second worker then completes this remaining work in 6 days (10 days - 4 days). Therefore, the second worker's work rate is (2/3)W divided by 6 days, which is (1/9)W per day.

Now, we can set up an equation to represent the work rates:

Work rate of the first worker + Work rate of the second worker = Combined work rate

Let's denote the number of days it takes for the first worker to complete the task individually as "x" and the number of days it takes for the second worker to complete the task individually as "y".

The work rate of the first worker is 1/x of the total work per day, and the work rate of the second worker is 1/y of the total work per day.

Using the equation above, we can write:

(1/x) + (1/y) = 1/4 (Equation 1)

We also know that the work rate of the second worker is (1/9)W per day. Since the work rate is inversely proportional to the number of days, we can write:

(1/y) = (1/9)W (Equation 2)

Now, we can solve these two equations to find the values of "x" and "y".

Solution Steps

1. Substitute the value of (1/y) from Equation 2 into Equation 1: (1/x) + (1/9)W = 1/4

2. Multiply both sides of the equation by 36x to eliminate the denominators: 9 + 4xW = 9x

3. Rearrange the equation to isolate the variable terms: 4xW - 9x = -9

4. Factor out the common term "x": x(4W - 9) = -9

5. Divide both sides of the equation by (4W - 9): x = -9 / (4W - 9)

6. Similarly, substitute the value of (1/x) from Equation 1 into Equation 2: (1/4) + (1/y) = 1/9

7. Multiply both sides of the equation by 36y to eliminate the denominators: 9y + 4yW = 4y

8. Rearrange the equation to isolate the variable terms: 4yW - 9y = -4y

9. Factor out the common term "y": y(4W - 9) = -4y

10. Divide both sides of the equation by (4W - 9): y = -4y / (4W - 9)

Now, we have expressions for the number of days each worker would take to complete the task individually. However, we need additional information about the value of "W" (the total work) to calculate the exact number of days. The given problem does not provide this information, so we cannot determine the specific values of "x" and "y" without further details.

Please provide the value of "W" (the total work) so that we can calculate the number of days each worker would take to complete the task individually.