Question

Из Москвы в Вологду одновременно вышли два юноши. Один проходит в день 40 верст, а второй 45 верст. Один прибыл в Вологду на один день раньше второго. Сколько верст от Москвы до Вологды?

Answer 1

Скорость первого 1/40 , а второго - 1/45
Соответсвенно первый шёл 9 дней, а второй 8 (до того момента, как они встретились).
Расстояние равно 360 верст
(40x9=360 и 45х8=360)

Answer 2

Problem Analysis

We are given that two young men simultaneously left Moscow for Vologda. One of them travels at a speed of 40 versts per day, while the other travels at a speed of 45 versts per day. We are also told that one of them arrived in Vologda one day earlier than the other. We need to determine the distance in versts from Moscow to Vologda.

Solution

Let's assume that the distance from Moscow to Vologda is D versts.

We know that the first young man travels at a speed of 40 versts per day. Therefore, the time taken by the first young man to travel from Moscow to Vologda is D/40 days.

Similarly, the second young man travels at a speed of 45 versts per day. Therefore, the time taken by the second young man to travel from Moscow to Vologda is D/45 days.

We are given that one of them arrived in Vologda one day earlier than the other. This means that the time taken by the first young man is one day less than the time taken by the second young man.

Using this information, we can set up the following equation:

D/40 = D/45 - 1

To solve this equation, we can multiply both sides by 40 * 45 to eliminate the denominators:

45D = 40D - 40 * 45

Simplifying the equation:

5D = 40 * 45

Dividing both sides by 5:

D = 40 * 9 = 360

Therefore, the distance from Moscow to Vologda is 360 versts.

Answer

The distance from Moscow to Vologda is 360 versts.