Question

первый рабочий, работая один, выполняет работу за 2 целые 1/2 дня, а второй рабочий, работая один, выполняет эту же работу за 3 целые 3/4 дня. за сколько дней выполнят эту работу оба рабочих, работая совместно?

Answer 1

1 - это вся работа, х - искомое время

1: 2 5/10 * х + 1: 3 3/4 * х = 1

(2/5+4/15) * х = 1

(6/15+4/15) * х = 1

х = 1: 10/15

х = 15/10 полтора дня

 

Может, так?

Answer 2

2 1/2+3 3/4=2 2/4+3 3/4=5 5/4=6 1/4(д.)

Ответ:за 6 1/4дней выполнят эту работу оба рабочих.

Answer 3

Problem Analysis

We have two workers who can complete a task individually in different amounts of time. We need to determine how long it will take for both workers to complete the task if they work together.

Worker 1's Time

According to the information provided, the first worker takes 2 and 1/2 days to complete the task when working alone.

Worker 2's Time

The second worker takes 3 and 3/4 days to complete the same task when working alone.

Calculation

To find out how long it will take for both workers to complete the task together, we need to find the least common multiple (LCM) of the two individual times.

Finding the LCM

The LCM of two numbers is the smallest number that is divisible by both numbers without leaving a remainder.

To find the LCM of 2 and 1/2 and 3 and 3/4, we need to convert the fractions to a common denominator. The common denominator of 2 and 1/2 and 3 and 3/4 is 4.

Converting 2 and 1/2 to an improper fraction: 2 and 1/2 = 2 + 1/2 = 4/2 + 1/2 = 5/2

Converting 3 and 3/4 to an improper fraction: 3 and 3/4 = 3 + 3/4 = 12/4 + 3/4 = 15/4

Now, we can find the LCM of 5/2 and 15/4.

The LCM of 5/2 and 15/4 is 15/2.

Final Answer

Therefore, it will take both workers working together a total of 15/2 days to complete the task.