Question

старший брат и младший брат и сестра слепили снеговика за12 мин. старший брат может его слепить за 24 мин. младший за 40. за сколько минут может слепить снеговика сестра?

Answer 1

1) 1\24 снеговика слепит старший брат за одну минуту

2) 1\40 снеговика слепит младший брат за одну минуту

3) 1\12 снеговика слепят старший брат, младший брат и сестренка вместе за одну минуту

4) 1\12-1\24-1\40=2\24-1\24-1\40=1\24-1\40=5\120-3\120=2\120=1\60 снеговика слепит сестра за одну минуту

5)1:1\60=60 мин - нужно сестре чтобы слепить снеговика

овтет: за 60 минут может слепить снеговика сестра (за 1 час)

Answer 2

Problem Analysis

We are given that the older brother can build a snowman in 24 minutes, the younger brother can build a snowman in 40 minutes, and they both built a snowman together in 12 minutes. We need to determine how long it would take the sister to build a snowman.

Solution

Let's assume that the sister's rate of building a snowman is S snowmen per minute. We can use the concept of "work done" to solve this problem. The work done by the older brother in 1 minute is 1/24 of a snowman, the work done by the younger brother in 1 minute is 1/40 of a snowman, and the work done by the sister in 1 minute is 1/S of a snowman.

Since the older brother and the younger brother built a snowman together in 12 minutes, their combined work is equal to 1 snowman. We can write the equation:

(1/24 + 1/40) * 12 = 1

Simplifying this equation, we get:

(5/120 + 3/120) * 12 = 1 (8/120) * 12 = 1 (2/30) * 12 = 1 (1/15) * 12 = 1 12/15 = 1 4/5 = 1

Therefore, the equation is true.

Now, we can determine the sister's rate of building a snowman:

1/S = 4/5

Cross-multiplying, we get:

5 = 4S

Dividing both sides by 4, we get:

S = 5/4

Therefore, the sister's rate of building a snowman is 5/4 snowmen per minute.

To determine how long it would take the sister to build a snowman, we can calculate the reciprocal of her rate:

1 / (5/4) = 4/5

Therefore, it would take the sister 4/5 minutes to build a snowman.

Answer

It would take the sister 4/5 minutes to build a snowman.

Explanation

The older brother can build a snowman in 24 minutes, the younger brother can build a snowman in 40 minutes, and they both built a snowman together in 12 minutes. By using the concept of "work done," we can determine that the sister's rate of building a snowman is 5/4 snowmen per minute. Therefore, it would take the sister 4/5 minutes to build a snowman.