Question

Слесарь, работая вместе с учеником, собирался выполнить некоторый заказ за 30 дней. После 6 дней совместной работы ученик уводился и слесарь, работая ещё 40 дней, закончил выполнение заказа. За сколько дней слесарь, работая один, может выполнить этот заказ? P.S. Помогите, пожалуйста, составить только систему уравнений (или не систему), решу я её самостоятельно.

Answer 1

Всю работу можно считать за 1-цу. Пусть х- производительность слесаря, а у - ученика. Их совместная производительность будет (х+у). Т.к. они предполагали работать вместе 30 дней и выполнить всю работу, получим 1-е уравнение 30*(х+у)=1.

Но фактически за 6 дней они сделали 6*(х+у) и 40х сделал слесарь сам.

Т.е. 6*(х+у)+40х=1  Получим систему

30*(х+у)=1

6*(х+у)+40х=1

Answer 2

Problem Analysis

To solve this problem, we need to determine how many days it would take for the locksmith to complete the order on his own. We are given that the locksmith and the apprentice were supposed to complete the order in 30 days, but after 6 days of working together, the apprentice left and the locksmith continued working for an additional 40 days to complete the order.

Let's assume that the locksmith's work rate is represented by L (in units of work per day) and the apprentice's work rate is represented by A (in units of work per day). We are also given that the combined work rate of the locksmith and the apprentice is sufficient to complete the order in 30 days.

Formulating the Equations

We can set up the following equation based on the given information:

Equation 1: (L + A) * 6 = 1 (The combined work rate of the locksmith and the apprentice multiplied by 6 days should equal the work done in those 6 days, which is 1 unit of work.)

We also know that the locksmith worked alone for an additional 40 days to complete the order. So, we can set up another equation:

Equation 2: L * 40 = 1 (The locksmith's work rate multiplied by 40 days should equal the remaining work, which is 1 unit of work.)

Solving the Equations

To solve this system of equations, we can first solve Equation 1 for A and then substitute that value into Equation 2.

From Equation 1, we can isolate A:

(L + A) * 6 = 1

Expanding the equation:

6L + 6A = 1

Isolating A:

6A = 1 - 6L

A = (1 - 6L) / 6

Now, we can substitute this value of A into Equation 2:

L * 40 = 1

Substituting A:

L * 40 = 1

Simplifying:

40L = 1

L = 1/40

Answer

The locksmith's work rate is 1/40 units of work per day. Therefore, working alone, the locksmith can complete the order in 40 days.

I hope this helps! Let me know if you have any further questions.