Question

Три экскаватора различной мощности могут вымыть котлован работая по отдельности первый за 10 дней, второй за 12 дней, третий за 15 дней. За сколько дней они могут выроют котлован, работая совместно

Answer 1

1/10 в день первый экскаватор
1/12 в день второй экскаватор
1/15 в день третий экскаватор
1/10+1/12+1/15= 6/60+5/60+4/60= 15/60= 1/4 котлована в день при работе сразу трёх экскаваторов.
1:1/4=1*4= 4
Ответ: за 4 дня выроют котлован три экскаватора

Answer 2

Problem Analysis

We are given three excavators of different power that can individually dig a pit in 10 days, 12 days, and 15 days, respectively. We need to determine how many days it will take for them to dig the pit together.

Solution

To solve this problem, we can calculate the rate at which each excavator digs the pit and then add up their rates to find the combined rate. Finally, we can use the combined rate to calculate the number of days required to dig the pit.

Let's denote the power of the first excavator as P1, the power of the second excavator as P2, and the power of the third excavator as P3. We are given that the first excavator can dig the pit in 10 days, the second excavator in 12 days, and the third excavator in 15 days.

The rate at which each excavator digs the pit can be calculated as the reciprocal of the number of days it takes for each excavator to dig the pit. Therefore, the rate at which the first excavator digs the pit is 1/10, the rate at which the second excavator digs the pit is 1/12, and the rate at which the third excavator digs the pit is 1/15.

To find the combined rate at which all three excavators dig the pit, we can add up their individual rates:

Combined rate = 1/10 + 1/12 + 1/15

Now, we can calculate the number of days required to dig the pit by dividing the total work (which is 1) by the combined rate:

Number of days required = 1 / (1/10 + 1/12 + 1/15)

Let's calculate the result.

Calculation

To calculate the number of days required to dig the pit, we need to find the combined rate of the three excavators and then divide the total work by the combined rate.

The combined rate of the three excavators is:

Combined rate = 1/10 + 1/12 + 1/15

Calculating the combined rate:

Combined rate = 0.1 + 0.0833 + 0.0667 = 0.25

Now, we can calculate the number of days required to dig the pit:

Number of days required = 1 / 0.25 = 4

Therefore, it will take the three excavators working together 4 days to dig the pit.

Answer

The three excavators, working together, can dig the pit in 4 days.

Explanation

When the three excavators work together, their combined rate is 0.25, which means they can dig 0.25 of the pit in one day. Since the total work is 1 (the entire pit), it will take them 4 days to complete the job.

Please let me know if you need any further clarification.