Question

Две снегоуборочные машины вместе выполняют работу за 2 часа. первая снегоуборочная самостоятельно может выполнить работу за 3 часа. за сколько время работу выполнит вторая снегоуборочная машина?

Answer 1

Производительность - часть работы за час.
1 машина имеет производительность - 1/3 (1:3ч.)
2 машина - 1/х;   (за х часов 2-я машина сделает всю работу);

Обе - 1/2; значит
1/2=1/3+1/х;
1/х=1/2-1/3;
1/х=(3-2)/6;
1/х=1/6
х=6 часов.
Проверка: 1/3+1/6=2/6+1/6=3/6=1/2 часть работы за час.
За 2 часа (1/2)*2=1 - вся работа за 2 часа.
Ответ: за 6 часов.

Answer 2

Problem Analysis

We are given that two snowplows can complete a job together in 2 hours. The first snowplow can complete the job alone in 3 hours. We need to determine how long it will take for the second snowplow to complete the job on its own.

Solution

Let's assume that the second snowplow can complete the job alone in x hours. We can use the concept of work rates to solve this problem.

The work rate of a snowplow is the amount of work it can complete in one hour. If the first snowplow can complete the job alone in 3 hours, its work rate is 1/3 of the job per hour. Similarly, if the second snowplow can complete the job alone in x hours, its work rate is 1/x of the job per hour.

When the two snowplows work together, their work rates are additive. So, the combined work rate of the two snowplows is 1/3 + 1/x of the job per hour.

We are given that the two snowplows can complete the job together in 2 hours. This means that their combined work rate is 1/2 of the job per hour.

Now we can set up an equation to solve for x, the number of hours it takes for the second snowplow to complete the job alone:

1/3 + 1/x = 1/2

To solve this equation, we can multiply both sides by 6x to eliminate the fractions:

2x + 6 = 3x

Simplifying the equation, we get:

6 = x

Therefore, the second snowplow can complete the job alone in 6 hours.

Answer

The second snowplow will take 6 hours to complete the job on its own.