Question

696; Старинная задача (Китай, I в. н. э.). Дикая утка от южного моря до северного летит 7 дней. Дикий гусь от северного моря до южного летит 9 дней. Через сколько дней они встретятся, если вылетят одновременно? ​

Answer 1

Ответ:

Пошаговое объяснение:

1/7+1/9=(9+7)/63=16/63 - скорость сближения .

t=1: 16/63=63/16=3 15/16 дней.

Answer 2

Problem Analysis

This is a classic problem that involves the flight paths of a wild duck and a wild goose. The duck flies from the southern sea to the northern sea in 7 days, while the goose flies from the northern sea to the southern sea in 9 days. We need to determine how many days it will take for them to meet if they both start flying at the same time.

Solution

To solve this problem, we can use the concept of relative speed. Let's assume that the distance between the southern sea and the northern sea is D.

The duck flies from the southern sea to the northern sea in 7 days, so its speed can be calculated as D/7. Similarly, the goose flies from the northern sea to the southern sea in 9 days, so its speed can be calculated as D/9.

When the duck and the goose start flying at the same time, they will meet when the sum of the distances they have traveled is equal to the total distance between the seas.

Let's denote the number of days it takes for them to meet as T. During this time, the duck will have traveled a distance of (D/7) * T, and the goose will have traveled a distance of (D/9) * T.

According to the problem, the sum of these distances should be equal to the total distance between the seas, which is D. Therefore, we can set up the following equation:

(D/7) * T + (D/9) * T = D

To solve this equation, we can simplify it by multiplying both sides by the least common multiple of 7 and 9, which is 63:

9 * (D/7) * T + 7 * (D/9) * T = 63 * D

Simplifying further, we get:

9D * T/7 + 7D * T/9 = 63D

Now, we can cancel out the common factors:

9D * T + 7D * T = 63D * 1

Combining like terms:

16D * T = 63D

Dividing both sides by 16D:

T = 63D / 16D

Simplifying:

T = 63 / 16

Therefore, it will take approximately 3.9375 days for the duck and the goose to meet if they both start flying at the same time.

Answer

If the wild duck and the wild goose start flying at the same time, they will meet approximately 3.9375 days later.

Note: The solution provided is based on the information given in the problem statement.