Question

Сестра вышла из дома, и через 6 минут после её выхода вслед за нею вышел её брат. Брат догнал сестру через 6 минут после своего выхода. Через сколько минут после своего выхода брат догнал бы сестру, если бы сестра шла в 2 раза медленнее?

Answer 1

Ответ:

Через 2 минуты.

Решение.   Так как брат прошёл за 6 минут такое же расстояние, какое прошла сестра за 12

                   минут, то её скорость в 2 раза меньше скорости брата. Если бы сестра шла ещё

                   в 2 раза медленнее, то скорость брата была бы в 4 раза больше.

                   Обозначим через t время, за которое брат догонит сестру, если она будет идти

                   2 раза медленнее, через х – скорость сестры, тогда 4xt=(6+t)x, t=2.

Пошаговое объяснение:

Answer 2

Problem Analysis

We are given that a sister left the house, and 6 minutes later her brother followed her. The brother caught up with the sister 6 minutes after he left the house. We need to determine how many minutes after leaving the house the brother caught up with the sister if the sister walked at half her original speed.

Solution

Let's assume that the sister's original speed is x units per minute. Since the brother caught up with the sister 6 minutes after he left the house, we can set up the following equation:

Distance covered by the sister = Distance covered by the brother + Distance covered by the sister in 6 minutes

The distance covered by the sister is x * t, where t is the time in minutes after the sister left the house. The distance covered by the brother is 2x * (t + 6), since the brother walks at twice the speed of the sister and starts 6 minutes later.

Setting up the equation:

x * t = 2x * (t + 6)

Simplifying the equation:

xt = 2xt + 12x

Subtracting 2xt from both sides:

xt - 2xt = 12x

Simplifying further:

-xt = 12x

Dividing both sides by x:

-t = 12

Multiplying both sides by -1:

t = -12

Since time cannot be negative, we can conclude that there is no solution to this problem. The brother will not be able to catch up with the sister if she walks at half her original speed.

Answer

If the sister walks at half her original speed, the brother will not be able to catch up with her.