Question

Двое рабочих должны были выполнить задание за 24 часа. После 16 часов совместной работы первы рабочий подучил новое задание, поэтому второй для окончания задания проработал еще 14 часов. за какое время мог выполнить задание каждый из рабочих, работая отдельно? Решить задачу при помощи уравнения или системы уравнений.

Answer 1

Problem Analysis

Two workers were initially given a task to complete within 24 hours. After working together for 16 hours, the first worker received a new task, so the second worker continued working for an additional 14 hours to complete the task. We need to determine how long each worker would take to complete the task individually.

Solution

Let's assume that the first worker can complete the task in x hours, and the second worker can complete the task in y hours.

From the given information, we can create the following equation: - The first worker worked for 16 hours and then stopped, so the amount of work completed by the first worker is 16/x. - The second worker worked for 16 hours with the first worker and then worked for an additional 14 hours, so the amount of work completed by the second worker is (16 + 14)/y.

Since the total work required to complete the task is 1 (the whole task), we can set up the equation: 16/x + (16 + 14)/y = 1

Now, we can solve this equation to find the values of x and y.

Solving the Equation

To solve the equation, we can simplify it by finding a common denominator and combining the fractions: (16y + 30x)/(xy) = 1

Cross-multiplying, we get: 16y + 30x = xy

Rearranging the equation, we have: xy - 30x - 16y = 0

Factoring out the common factor of x and y, we get: x(y - 30) - 16(y - 30) = 0

Simplifying further, we have: (x - 16)(y - 30) = 0

This equation can be satisfied if either (x - 16) = 0 or (y - 30) = 0.

If (x - 16) = 0, then x = 16. This means that the first worker can complete the task in 16 hours.

If (y - 30) = 0, then y = 30. This means that the second worker can complete the task in 30 hours.

Therefore, the first worker can complete the task individually in 16 hours, and the second worker can complete the task individually in 30 hours.

Answer

The first worker can complete the task individually in 16 hours, and the second worker can complete the task individually in 30 hours.