Question

Моторная лодка проплыла по течению реки 18 км , а затем против течения- 30 км. При этом на весь путь она затратила 8 часов.Найдите собственную скорость лодки , если скорость течения реки равна 2км/ч

Answer 1

Пусть х -собственная скорость лодки,скорость по течению:(х+2)км/ч
против течения:(х-2)км/ч
время по течению:18/(х+2)
время против течения:30/(х-2)
получается уравнение:
18/(х+2)+30/(х-2)=8
домножим на (х+2)(х-2) и избавимся от знаменателя:
18(х-2)+30(х+2)=8(х-2)(х+2)
18х-36+30х+60=(8х-16)(х+2)
48х+24=8х^2+16х-16х-32
-8x^2+32+48x+24=0
-8x^2+48x+56=0
8x^2-48x-56=0
x^2-6x-7=0
{x1+x2=6;x1=-1(не подходит)
{x1*x2=-7;x2=7
ответ:7 км/ч

Answer 2

X - собственная скорость лодки; (x +2) - скорость по течению; (x-2)-против течения;
 (18 / (x+2) ) - время , которое лодка шла по течению; (30 / (x -2) ) - шла против течения, известно, что на весь путь она затратила 8ч =>
(18/(x+2) ) +  (30 / (x -2) ) = 8; *(x+2)(x-2);
18 * (x-2) + 30 * (x+2) = 8*(x+2)(x-2)
18x - 36 + 30x + 60 = 8x^2 - 4 * 8
-8x^2 + 48x + 56 = 0 (/8)
x^2 - 6x - 7 = 0
x1 = 7
x2 = -1, не подходит!
Ответ:7км/ч

Answer 3

Problem Analysis

We are given the following information: - The motorboat traveled downstream for 18 km. - The motorboat then traveled upstream for 30 km. - The total time taken for the entire journey was 8 hours. - The speed of the river current is 2 km/h.

We need to find the speed of the motorboat.

Solution

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

When the motorboat is traveling downstream, its effective speed is the sum of its own speed and the speed of the river current. Therefore, the effective speed downstream is (x + 2) km/h.

When the motorboat is traveling upstream, its effective speed is the difference between its own speed and the speed of the river current. Therefore, the effective speed upstream is (x - 2) km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

The time taken to travel downstream is given by 18 km = (x + 2) km/h × t1.

The time taken to travel upstream is given by 30 km = (x - 2) km/h × t2.

We also know that the total time taken for the entire journey is 8 hours, so t1 + t2 = 8.

We can solve these equations to find the value of x.

Calculation

Let's solve the equations:

From the equation 18 km = (x + 2) km/h × t1, we can rearrange it to get t1 = 18 km / (x + 2) km/h.

From the equation 30 km = (x - 2) km/h × t2, we can rearrange it to get t2 = 30 km / (x - 2) km/h.

Substituting these values into the equation t1 + t2 = 8, we get 18 km / (x + 2) km/h + 30 km / (x - 2) km/h = 8.

To solve this equation, we can multiply through by (x + 2)(x - 2) to eliminate the denominators:

18 km(x - 2) + 30 km(x + 2) = 8(x + 2)(x - 2).

Expanding and simplifying the equation, we get 18x - 36 + 30x + 60 = 8(x^2 - 4).

Simplifying further, we get 48x + 24 = 8x^2 - 32.

Rearranging the equation, we get 8x^2 - 48x - 56 = 0.

We can solve this quadratic equation to find the value of x.

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 8, b = -48, and c = -56.

Calculating the values, we get x = 7 or x = -1.

Since the speed of the motorboat cannot be negative, the speed of the motorboat is 7 km/h.

Answer

The speed of the motorboat is 7 km/h.