Question

Моторная лодка прошла 28 км против течения реки и 16 км по течению, затратив на весь путь 3 час . Какова скорость моторной лодки в стоячей воде , если скорость течения реки равна 1км/ч ?

Answer 1

Х км/ч - скорость лодки
х+1 км/ч - скорость по течению
х-1  км/ч - скорость против течения

28/(х-1)+16/(х+1)=3
28(х+1)+16(х-1)=3(х+1)(х-1)
28х+28+16х-16=3х²-3
3х² - 44х - 13=0
D/4=22²+3*13=523≈+-23²
х1=(22-23)/3= - 1/3 - не подходит решению
х2=(22+23)/3=15(км/ч) - скорость катера

Answer 2

Problem Analysis

We are given that a motorboat traveled 28 km against the current of a river and 16 km with the current, taking a total of 3 hours for the entire journey. We need to find the speed of the motorboat in still water, given that the speed of the river current is 1 km/h.

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 reduced by the speed of the current. So, the speed of the motorboat against the current is (x - 1) km/h.

When the motorboat is traveling with the current, its effective speed is increased by the speed of the current. So, the speed of the motorboat with the current is (x + 1) 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 28 km against the current is given by: 28 = (x - 1) × t1 The time taken to travel 16 km with the current is given by: 16 = (x + 1) × t2 We are also given that the total time for the entire journey is 3 hours: t1 + t2 = 3 We can solve this system of equations to find the value of x, the speed of the motorboat in still water.

Solution Steps

1. Rearrange equation to solve for t1: t1 = 28 / (x - 1)

2. Rearrange equation to solve for t2: t2 = 16 / (x + 1)

3. Substitute the values of t1 and t2 into equation 28 / (x - 1) + 16 / (x + 1) = 3

4. Solve the equation for x.

Let's perform the calculations to find the speed of the motorboat in still water.

Calculation

Substituting the values of t1 and t2 into equation we get: 28 / (x - 1) + 16 / (x + 1) = 3

Multiplying through by the least common multiple of the denominators, we get: 28(x + 1) + 16(x - 1) = 3(x - 1)(x + 1)

Expanding and simplifying the equation, we get: 28x + 28 + 16x - 16 = 3(x^2 - 1)

Combining like terms, we get: 44x + 12 = 3x^2 - 3

Rearranging the equation, we get: 3x^2 - 44x - 15 = 0

Using the quadratic formula, we can solve for x: x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values of a, b, and c into the quadratic formula, we get: x = (-(-44) ± √((-44)^2 - 4(3)(-15))) / (2(3))

Simplifying the equation, we get: x = (44 ± √(1936 + 180)) / 6

Calculating the values inside the square root, we get: x = (44 ± √(2116)) / 6

Simplifying the equation further, we get: x = (44 ± 46) / 6

Calculating the values inside the parentheses, we get two possible values for x: x1 = (44 + 46) / 6 = 90 / 6 = 15 x2 = (44 - 46) / 6 = -2 / 6 = -1/3

Since the speed of the motorboat cannot be negative, we discard the negative value of x.

Answer

The speed of the motorboat in still water is 15 km/h.

Explanation

The motorboat's speed in still water is 15 km/h. When traveling against the current, its effective speed is reduced by the speed of the current (1 km/h), resulting in a speed of 14 km/h. When traveling with the current, its effective speed is increased by the speed of the current, resulting in a speed of 16 km/h. These speeds allow the motorboat to cover the distances of 28 km and 16 km, respectively, in the given times of 2 hours and 1 hour. The total time for the entire journey is 3 hours, as given.

Note

Please note that the calculations provided above are based on the given information and assumptions made. If there are any additional factors or constraints that need to be considered, please provide them for a more accurate analysis.