Question

Рабочий и его ученик работая вместе могут закончить работу за 14 часов .если сначала 7/9 работы выполнит рабочий ,а затем оставшуюся работу выполнит ученик то вся работа будет выполнена за 28 часов.За сколько часов сможет выполнить всю работу один рабочий

Answer 1

Допустим, что рабочий выполнит всю работу за х часов, а ученик  - за у часов.  

За час рабочий 1/х часть работы, а ученик - 1/у

согласно этим данным можно составить систему уравнений:

14(1/х+1/у)=1-  вся работа

(7/9)х+(2/9)у=28 - часов

14у+14х=ху       

у=126-3,5х                           

3,5x2-161x+1764=0

D=25921-24696=1225

x₁=18,  x₂=28 - не удовлетворяет условию.

у=126-3,5·18=126-63=63

Ответ: за 18 часов  рабочий, а за 63 - ученик.

Answer 2

Problem Analysis

We are given that a worker and their apprentice can complete a job together in 14 hours. If the worker completes 7/9 of the job first, and then the apprentice completes the remaining work, the entire job is completed in 28 hours. We need to determine how long it would take for the worker to complete the entire job alone.

Solution

Let's assume that the worker's rate of work is W (in units of job per hour) and the apprentice's rate of work is A (in units of job per hour).

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

1. When the worker completes 7/9 of the job and the apprentice completes the remaining 2/9 of the job, the total time taken is 14 hours: - (7/9) / W + (2/9) / A = 14

2. When the worker completes the entire job alone, the total time taken is T hours: - 1 / W = T

To find the value of T, we can solve these equations simultaneously.

Solving the Equations

Let's solve the equations using substitution.

From equation 2, we can express A in terms of W: - A = 1 / T

Substituting this value of A into equation 1, we get: - (7/9) / W + (2/9) / (1 / T) = 14

Simplifying the equation: - (7/9) / W + (2/9) * T = 14

Multiplying both sides of the equation by 9: - 7 / W + 2 * T = 126

Rearranging the equation: - 7 / W = 126 - 2 * T

Dividing both sides of the equation by 7: - 1 / W = (126 - 2 * T) / 7

Taking the reciprocal of both sides of the equation: - W = 7 / (126 - 2 * T)

Now, we can substitute this value of W into equation 2 to find T: - 1 / (7 / (126 - 2 * T)) = T

Simplifying the equation: - (126 - 2 * T) / 7 = T

Multiplying both sides of the equation by 7: - 126 - 2 * T = 7 * T

Rearranging the equation: - 126 = 7 * T + 2 * T

Combining like terms: - 126 = 9 * T

Dividing both sides of the equation by 9: - T = 14

Answer

Therefore, it would take the worker 14 hours to complete the entire job alone.