Question

Моторная лодка прошла против течения реки 91 км/ч и вернулась в пункт отправления, затратив на обратный путь на 6 часов меньше. Найти скорость течения, если скорость в неподвижной воде равна 10 км/ч.

Answer 1

Пусть х- скорость течения, тогда скорость лодки по течению 10+х, а против 10-х, время затраченное на дорогу против течения 91/(10-х), а время по течению 91/(10+х) По условию разность по времени 6 часов, составим уравнение:
91/(10-х)-91/(10+х)=6
910+91х-910+91х=600-6х^2
6х^2+182x-600=0
3х^2+91x-300=0
x=3

Answer 2

Problem Analysis

We are given the following information: - The speed of the motorboat against the current is 91 km/h. - The motorboat returns to the starting point, spending 6 hours less on the return journey. - The speed of the current is 10 km/h.

We need to find the speed of the current.

Solution

Let's assume the speed of the motorboat in still water is x km/h.

When the motorboat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the effective speed is (x - 10) km/h.

We are given that the motorboat takes 6 hours less to return to the starting point. This means that the time taken to travel downstream (with the current) is 6 hours less than the time taken to travel upstream (against the current).

Let's calculate the time taken to travel upstream and downstream.

The distance traveled upstream is the same as the distance traveled downstream, as the motorboat returns to the starting point. Let's assume this distance is d km.

The time taken to travel upstream is given by the equation:

Time taken upstream = Distance / Speed upstream

The time taken to travel downstream is given by the equation:

Time taken downstream = Distance / Speed downstream

Since the distance is the same for both directions, we can set up the following equation:

Distance / (x - 10) = Distance / (x + 10 - 6)

Simplifying the equation, we get:

1 / (x - 10) = 1 / (x + 4)

Cross-multiplying, we get:

(x - 10) * (x + 4) = 1

Expanding the equation, we get:

x^2 - 6x - 40 = 0

Solving this quadratic equation will give us the value of x, which represents the speed of the motorboat in still water. Once we have the value of x, we can calculate the speed of the current by subtracting 10 km/h from x.

Let's solve the quadratic equation to find the value of x.

Calculation

Using the quadratic formula, we have:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 - 6x - 40 = 0, the values of a, b, and c are:

a = 1 b = -6 c = -40

Substituting these values into the quadratic formula, we get:

x = (-(-6) ± √((-6)^2 - 4(1)(-40))) / (2(1))

Simplifying further, we get:

x = (6 ± √(36 + 160)) / 2

x = (6 ± √196) / 2

x = (6 ± 14) / 2

We have two possible solutions for x:

1. x = (6 + 14) / 2 = 20 / 2 = 10 2. x = (6 - 14) / 2 = -8 / 2 = -4

Since the speed of the motorboat cannot be negative, we discard the second solution.

Therefore, the speed of the motorboat in still water is 10 km/h.

To find the speed of the current, we subtract 10 km/h from the speed of the motorboat in still water:

Speed of current = Speed of motorboat in still water - Speed of motorboat against the current

Speed of current = 10 km/h - 10 km/h = 0 km/h

Therefore, the speed of the current is 0 km/h.

Answer

The speed of the current is 0 km/h.