Question

Аня и Катя вырезают снежинки к новому году.Вместе они сделали всю работу за 3 3/4часа.Одна Аня сможет сделать эту работу за 6 часов.За сколько времени могла бы выпезать все снежинки Катя?

Answer 1

Ну я думаю так ))))))))

Answer 2

Calculation of Time for Both Anna and Katya

To find out how long it would take Katya to complete all the snowflakes, we can use the information given in the question.

Let's assume that Anna's work rate is represented by the variable "A" (in units of snowflakes per hour) and Katya's work rate is represented by the variable "K" (in units of snowflakes per hour).

According to the question, Anna can complete the entire job in 6 hours. Therefore, we can say that Anna's work rate is 1/6 of the job per hour, or A = 1/6.

The combined work rate of Anna and Katya is given as 1 job per 3 3/4 hours. We can convert this to a fraction of the job per hour by taking the reciprocal: 1 / (3 3/4) = 4/15. Therefore, the combined work rate of Anna and Katya is 4/15 of the job per hour, or A + K = 4/15.

To find Katya's work rate, we can subtract Anna's work rate from the combined work rate: K = (A + K) - A = 4/15 - 1/6.

Now we can calculate Katya's work rate:

K = (4/15) - (1/6) = (8/30) - (5/30) = 3/30 = 1/10.

This means that Katya can complete 1/10 of the job per hour.

Time for Katya to Complete All the Snowflakes

To find out how long it would take Katya to complete all the snowflakes, we can set up a proportion using her work rate.

Let's assume that the total number of snowflakes is represented by the variable "S" (in units of snowflakes). Since Anna and Katya together can complete the entire job in 3 3/4 hours, we can say that the total number of snowflakes is equal to their combined work rate multiplied by the time taken:

S = (A + K) * (3 3/4).

Substituting the values we found earlier:

S = (1/6 + 1/10) * (3 3/4).

To simplify the calculation, we can convert the mixed number 3 3/4 to an improper fraction: 3 3/4 = (4 * 3 + 3) / 4 = 15/4.

S = (1/6 + 1/10) * (15/4).

To add the fractions, we need a common denominator, which is 30:

S = (5/30 + 3/30) * (15/4) = 8/30 * 15/4.

Multiplying the fractions:

S = (8 * 15) / (30 * 4) = 120 / 120 = 1.

Therefore, the total number of snowflakes is 1.

Since Katya's work rate is 1/10 of the job per hour, it would take her 10 hours to complete all the snowflakes.