Question

Послан гонец из Москвы в Волгоград, и велено ему в хождении своём совершать во всякий день по 40 вёрст. На следующий день ему был послан второй гонец, и приказано ему проходить в день по 45 вёрст. На какой день второй гонец догонит первого???

Answer 1

Второй гонец проходит на 5 верст больше первого. Для того, чтобы ему догнать первого, он должен пройти за все дни, пока не догонит его, на 40 верст больше, (то есть в первый день на 5 верст, во второй уже на 10, а в третий на 15 верст пройдет больше и так до 40 верст) 40 : 5 = 8 дней
Ответ: за 8 дней

Answer 2

Problem Analysis

The problem states that a messenger is sent from Moscow to Volgograd and is ordered to travel 40 versts each day. On the next day, a second messenger is sent and is ordered to travel 45 versts each day. We need to determine on which day the second messenger will catch up to the first messenger.

Solution

To solve this problem, we can set up an equation based on the distances traveled by each messenger. Let's assume that the first messenger catches up to the second messenger on day `x`.

On day `x`, the first messenger would have traveled a total distance of `40x` versts, and the second messenger would have traveled a total distance of `45(x-1)` versts (since the second messenger starts one day later).

Since the first messenger catches up to the second messenger, the distances traveled by both messengers must be equal. Therefore, we can set up the following equation:

40x = 45(x-1)

Simplifying the equation:

40x = 45x - 45
5x = 45
x = 9

Therefore, the second messenger will catch up to the first messenger on the 9th day.

Answer

The second messenger will catch up to the first messenger on the 9th day.