Question

Два экскаватора,работая совместно могут вырыть котлован за 48 часов если первый проработает 40 ч а второй 30 ч то будет выполнено 75% всей работы за какое время может вырыть котлован второй экскаватор работая отдельно ?

Answer 1

Составим уравнения по условию задачи
48(x+y)=1
40x+30y=0.75

преобразуем второе уравнение
48x+48y=1
160/3x+40y=1

приравняем левые части уравнений друг к другу и выразим одну переменную через другую
8y=16/3x
y=2/3x

найдем значение первой переменной
48×5/3x=1
80x=1
x=1/80
найдем знание второй переменной
y=1/120
1/(1/120)=120

второй экскаватор выкопает котлован за 120 часов

Answer 2

Problem Analysis

We are given that two excavators working together can dig a pit in 48 hours. The first excavator works for 40 hours, and the second excavator works for 30 hours. We need to determine how long it would take for the second excavator to dig the pit alone.

Solution

Let's assume that the rate at which the two excavators work together is 100% of the total work. Since the two excavators can complete the work in 48 hours, we can say that the total work is equal to 100%.

We are also given that the first excavator works for 40 hours, which is 83.33% of the total work (40/48 * 100). Similarly, the second excavator works for 30 hours, which is 62.5% of the total work (30/48 * 100).

To find out how long it would take for the second excavator to dig the pit alone, we need to determine the remaining percentage of work that the second excavator needs to complete. This can be calculated by subtracting the work done by the first excavator from the total work.

The remaining work for the second excavator can be calculated as follows: Remaining work = Total work - Work done by the first excavator

Substituting the values, we get: Remaining work = 100% - 83.33% = 16.67%

Now, we can calculate the time it would take for the second excavator to complete this remaining work. Since the second excavator works at a rate of 62.5% of the total work in 30 hours, we can set up a proportion to find the time it would take for the second excavator to complete 16.67% of the work.

Let x be the time it would take for the second excavator to complete the remaining work. The proportion can be set up as follows: 62.5/30 = 16.67/x

Simplifying the proportion, we get: 62.5x = 16.67 * 30

Solving for x, we find: x = (16.67 * 30) / 62.5

Calculating the value of x, we find that it would take the second excavator approximately 8 hours to complete the remaining work.

Therefore, the second excavator, working alone, would be able to dig the pit in approximately 8 hours.

Answer

The second excavator, working alone, would be able to dig the pit in approximately 8 hours.