Question

Моторная лодка проплывает некоторое расстояние по озеру за 40 минут,а такое же расстояние по течению реки она проплывает за 30 минут.За сколько минут моторная лодка проплывает такое же расстояние против течение реки? 1 СМОТРЕТЬ ОТВЕТ

Answer 1

s - расстояние, вводим для удобства

хл - скорость лодки

хт - скорость течения

скорость лодки через s

хл = s ÷ 2/3 = 1.5s

скорость течения через s

s ÷ (xл + хт) = 0.5

s = 0.5(1.5s + xт)

хт = 0.25s

а теперь считаем время

s ÷ (xл - хт) = s ÷ 1.25s = 0.8 часа

а 0.8 часа = 48 минут

Ответ: 48 мин.

Answer 2

Problem Analysis

We are given that a motorboat travels a certain distance across a lake in 40 minutes and the same distance downstream in a river in 30 minutes. We need to determine how long it will take for the motorboat to travel the same distance upstream against the river's current.

Solution

Let's assume that the distance the motorboat travels is d.

When the motorboat is traveling across the lake, it is not affected by any current, so its speed is constant. Let's denote the speed of the motorboat across the lake as v.

We can use the formula speed = distance / time to calculate the speed of the motorboat across the lake: v = d / 40 .

When the motorboat is traveling downstream in the river, it benefits from the current, which adds to its speed. Let's denote the speed of the river's current as c. The speed of the motorboat downstream is the sum of its own speed and the speed of the current, so we have: v + c = d / 30 .

To find the speed of the motorboat, we can subtract the speed of the current from the speed of the motorboat downstream: v = (d / 30) - c.

Now, when the motorboat is traveling upstream against the river's current, the current acts against its speed, so we subtract the speed of the current from the speed of the motorboat. Let's denote the time it takes for the motorboat to travel the same distance upstream as t. We can use the formula speed = distance / time to calculate the speed of the motorboat upstream: v - c = d / t.

Now we can solve for t by substituting the value of v from the previous equation: (d / 30) - c - c = d / t.

Simplifying the equation, we get: d / 30 - 2c = d / t.

Rearranging the equation, we have: d / t = d / 30 - 2c.

Now we can solve for t by equating the two sides of the equation: t = 30 / (1 - 2c / d).

Therefore, the motorboat will take 30 / (1 - 2c / d) minutes to travel the same distance upstream against the river's current.

Answer

The motorboat will take 30 / (1 - 2c / d) minutes to travel the same distance upstream against the river's current.

Please note that we do not have specific values for the distance d and the current speed c in the given question. Therefore, we cannot provide a numerical answer. However, the formula provided can be used to calculate the time based on the specific values of d and c.