Question

Трое рабочих должны выполнить некоторую работу.Первый рабочий может выполнить всю работу,работая один в 10 1/2 рабочих дней, а второй в 15 3/4 рабочих дня, а одному третьему рабочему потребуется в 3 1/3 раза больше рабочих дней, чем первым двум рабочим при их одновременной работе. Во сколько рабочих дней, работая все трое вместе, выполнят они работу?Решить подробно.

Answer 1

пусть вся работа   1, тогда за1 день 1рабочий  выполнит работу за 1:10 1/2=2/21части всей работы,  2 рабочий 1:15 3/4=4/63 ч. всей работы, вместе 2/21+4/63=10/63ч. возьмём за х кол-во дней их совместной работы и получим 10/63*х=1   х=63/10     далее 63/10*3   1/3=21 дней на всю работу 3 рабочему, а за 1 день  1/21ч всей работы. сост уравнение   (2/21+4/63+1/21)*х=1   х=4   11/13дней

Answer 2

Problem Analysis

We have three workers who need to complete a certain amount of work. The first worker can complete the work in 10 1/2 working days, the second worker can complete it in 15 3/4 working days, and the third worker will take 3 1/3 times longer than the first two workers combined. We need to determine how many working days it will take for all three workers to complete the work together.

Solution

To find the number of working days required for all three workers to complete the work together, we need to calculate the combined efficiency of the first two workers and then calculate the time required for the third worker.

Let's start by calculating the combined efficiency of the first two workers.

The first worker can complete the work in 10 1/2 working days, which is equivalent to 21/2 working days. The second worker can complete the work in 15 3/4 working days, which is equivalent to 63/4 working days.

To find the combined efficiency, we add the reciprocals of the individual efficiencies and take the reciprocal of the sum.

Combined efficiency = 1 / (1/efficiency of worker 1 + 1/efficiency of worker 2)

Let's calculate the combined efficiency:

Combined efficiency = 1 / (1/(21/2) + 1/(63/4))

To simplify the calculation, we can convert the mixed fractions to improper fractions:

Combined efficiency = 1 / (2/1 + 4/3)

Now, let's add the fractions:

Combined efficiency = 1 / (6/3 + 4/3) = 1 / (10/3) = 3/10

So, the combined efficiency of the first two workers is 3/10.

Now, let's calculate the time required for the third worker.

The third worker will take 3 1/3 times longer than the combined efficiency of the first two workers. Since the combined efficiency is 3/10, the third worker will take:

Time required for the third worker = (3 1/3) * (3/10)

To calculate this, we can convert the mixed fraction to an improper fraction:

Time required for the third worker = (10/3) * (10/10 + 1/3) = (10/3) * (11/10) = 110/30 = 11/3

So, the third worker will take 11/3 working days to complete the work.

Now, let's calculate the total time required for all three workers to complete the work together.

Total time required = Time required for the first two workers + Time required for the third worker

Time required for the first two workers = 21/2 + 63/4 = 42/4 + 63/4 = 105/4

Total time required = 105/4 + 11/3

To add these fractions, we need to find a common denominator:

Total time required = (105/4) * (3/3) + (11/3) * (4/4) = 315/12 + 44/12 = 359/12

So, all three workers will complete the work in 359/12 working days.

Answer

Therefore, all three workers will complete the work in approximately 29.92 working days when working together.

Please note that the calculations provided are based on the given information and assumptions made.