Question

Плот проплыл по реке из A в Б за 4 часа, а катер прошел из Б в А за 1 час. За сколько минут катер пройдет по реке из А в Б ? А) 30 Б) 40 В) 45 Г) 50 Д)55 Ответ с подробным решением.

Answer 1

Пусть S - расстояние от А до В.

v - собственная скорость катера

w - скорость течения, она же скорость плота

По условию, плот прошел расстояние S за 4 часа:

$\dfrac{S}{w} =4$

Сразу найдем соотношение для S:

$S=4w$

По условию, катер прошел из В в А (то есть против течения) за 1 час:

$\dfrac{S}{v-w} =1$

Подставим известное соотношение для S и найдем соотношение для v:

$\dfrac{4w}{v-w} =1$

$4w=v-w$

$v=5w$

Наконец, нужно найти время движения катера по течению:

$t=\dfrac{S}{v+w}$

Подставим известные соотношения для S и для v:

$t=\dfrac{4w}{5w+w} =\dfrac{4w}{6w} =\dfrac{4}{6} =\dfrac{2}{3}$

Полученный результат в часах переведем в минуты:

2/3 ч = 40 мин

Ответ: 40

Answer 2

Problem Analysis

We are given that a boat traveled from point A to point B in 4 hours, while a motorboat traveled from point B to point A in 1 hour. We need to determine how many minutes it will take for the motorboat to travel from point A to point B.

Solution

Let's assume that the distance between point A and point B is d.

We can use the formula: Speed = Distance / Time to find the speed of the boat and the motorboat.

The speed of the boat is given by: Speed of boat = d / 4.

The speed of the motorboat is given by: Speed of motorboat = d / 1.

Since the speed is inversely proportional to the time taken, we can set up the equation: Speed of boat = 1 / (Time taken by motorboat / 60).

Simplifying the equation, we get: d / 4 = 1 / (Time taken by motorboat / 60).

To find the time taken by the motorboat, we can solve for it.

Detailed Solution

Let's solve the equation to find the time taken by the motorboat.

d / 4 = 1 / (Time taken by motorboat / 60)

Multiplying both sides of the equation by (Time taken by motorboat / 60), we get:

d / 4 * (Time taken by motorboat / 60) = 1

Simplifying the equation, we get:

d * (Time taken by motorboat / 240) = 1

Multiplying both sides of the equation by 240, we get:

d * Time taken by motorboat = 240

Dividing both sides of the equation by d, we get:

Time taken by motorboat = 240 / d

Therefore, the time taken by the motorboat to travel from point A to point B is 240 / d.

To find the answer, we need to determine the value of d.

Unfortunately, the given information does not provide the value of d or any other information that can help us determine it. Therefore, we cannot determine the exact time taken by the motorboat to travel from point A to point B.

Hence, the answer cannot be determined with the given information.

Answer

The answer cannot be determined with the given information.