Question

Моторная лодка шла по течению реки со скоростью 16 километров в час а против течения со скоростью 14 км в час найдите скорость течения реки Измените данные задачи так чтобы получить в ответе скорость течения реки которая равна 500 метров в час

Answer 1

Problem Analysis

We are given the speed of a motorboat in still water and the speeds of the boat when going downstream and upstream. We need to find the speed of the river's current.

Solution

Let's assume the speed of the river's current is x km/h.

When the boat is going downstream, its effective speed is the sum of the boat's speed in still water and the speed of the current. So, the effective speed is 16 + x km/h.

When the boat is going upstream, its effective speed is the difference between the boat's speed in still water and the speed of the current. So, the effective speed is 14 - x km/h.

Since the distance traveled downstream and upstream is the same, we can set up the following equation:

Distance = Speed × Time

Let's assume the distance traveled is d km. The time taken to travel downstream is d / (16 + x) hours, and the time taken to travel upstream is d / (14 - x) hours.

Since the distance is the same, we can set up the equation:

d / (16 + x) = d / (14 - x)

To solve for x, we can cross-multiply and simplify the equation:

d(14 - x) = d(16 + x)

Simplifying further:

14d - dx = 16d + dx

Combining like terms:

14d - 16d = dx + dx

Simplifying:

-2d = 2dx

Dividing both sides by 2d:

-1 = x

Therefore, the speed of the river's current is -1 km/h.

Revised Problem

To obtain an answer of the river's current speed equal to 500 meters per hour, we can revise the problem as follows:

The boat's speed in still water is y km/h, and the speeds of the boat when going downstream and upstream are y + 16 km/h and y - 14 km/h, respectively.

Using the same approach as before, we can set up the equation:

d / (y + 16) = d / (y - 14)

Cross-multiplying and simplifying:

d(y - 14) = d(y + 16)

Simplifying further:

y - 14 = y + 16

Subtracting y from both sides:

-14 = 16

This equation is not possible to solve, as it leads to a contradiction. Therefore, it is not possible to find a boat speed in still water that would result in a river current speed of 500 meters per hour.