Question

Два слесаря за два часа совместной работы выполнили 65% за сколько часов может выполнить заказ каждый слесарь если одному из них требуется для этого на 3 часа больше чем другому

Answer 1

обозначим время, которое каждый затратит на самомтоятельное выполнение работы как х и у.

х = у+ 3 

Пусть вся работа- 1, тогда производительность каждого- 1/х  и  1/у

за 2 ч выполнено 0,65 всей работы.

Составим систему уравнений

$\left \{ {({ \frac{1}{x} + \frac{1}{y})2=0,65 } \atop {x=y+3}} \right.$

подставим значение х из второго уравнения в первое

${ {({ \frac{1}{y+3} + \frac{1}{y})2=0,65 }$  | умножим на 100y(y+3)

200y+200y+600=65y²+195y

-65y²+205y+600=0 | : 5

-13y²+41y+120=0

D=1681+4*13*120=7921

$y_{1} = \frac{-41+89}{-26} = -\frac{48}{26}$

$y_{2} = \frac{-41-89}{-26} =5$

x = 5+3 = 8

Ответ: каждый слесарь может выполнить заказ за 5 и 8 ч

Answer 2

Problem Analysis

We are given that two locksmiths completed 65% of a task in two hours of joint work. We need to determine how many hours each locksmith would take to complete the entire task individually, given that one locksmith requires 3 hours more than the other.

Solution

Let's assume that the first locksmith can complete the task in x hours. Since the second locksmith requires 3 hours more, they can complete the task in (x + 3) hours.

We are given that when they work together for 2 hours, they complete 65% of the task. This means that the combined work rate of the two locksmiths is 65% of the work rate required to complete the task.

To find the combined work rate, we can add the individual work rates of the locksmiths. The combined work rate is equal to the work done divided by the time taken. Therefore, we have the equation:

2(x + x + 3) = 0.65

Simplifying the equation:

4x + 6 = 0.65

4x = 0.65 - 6

4x = -5.35

x = -5.35 / 4

x ≈ -1.34

Since the number of hours cannot be negative, we can conclude that there is no valid solution to this problem.

Conclusion

Based on the given information, there is no valid solution to the problem. The negative value obtained for the number of hours indicates that the problem is not feasible.