Question

Двое рабочих, работая вместе, могут выполнить работу за 12 дней. За сколькодней, работая отдельно, выполнит эту работу первый рабочий, если он за двадня выполняет такую же часть работы, какую второй – за три дня?

Answer 1

работа = 1, x-раб. в день 1 рабочий, у - 2ой.

(х+у)12=1.

2х=3у. у=2х\3.

(2х\3+х)12=1.

20х=1. х=1\20. Т.е. за день 1 рабочий выполняет 1\20 работы, значит для выполнения всей работы ему понадобится 20 дней.

 

Answer 2

Problem Analysis

We are given that two workers can complete a job together in 12 days. We need to determine how many days it would take for the first worker to complete the job if they work alone, assuming they complete the same portion of the work in two days as the second worker does in three days.

Solution

Let's assume that the total work required to complete the job is represented by the variable "W". Since two workers can complete the job together in 12 days, we can say that their combined work rate is 1/12 of the total work per day.

Now, let's determine the work rate of the second worker. We know that the second worker completes the same portion of the work in three days as the first worker does in two days. Therefore, the work rate of the second worker is 2/3 of the work rate of the first worker.

Let's represent the work rate of the first worker as "x" (per day). Therefore, the work rate of the second worker would be (2/3)x (per day).

Since the work rate of the first worker is "x" and the work rate of the second worker is (2/3)x, we can write the equation:

x + (2/3)x = 1/12

Simplifying the equation, we get:

(5/3)x = 1/12

To solve for "x", we can multiply both sides of the equation by (3/5):

x = (1/12) * (3/5)

Simplifying further, we get:

x = 1/20

This means that the work rate of the first worker is 1/20 of the total work per day.

Now, let's determine how many days it would take for the first worker to complete the job alone. Since the work rate of the first worker is 1/20 of the total work per day, it would take the first worker 20 days to complete the job alone.

Answer

Therefore, if the first worker completes the same portion of the work in two days as the second worker does in three days, the first worker would take 20 days to complete the job alone.