Question

Расстояние от пункта А до пункта В теплоход проплыл против течения за 1ч 48 мин .На обратный путь из пункта В до пункта А он затратил на 18 мин меньше .Скорость течения реки 2,4 км/ч .Найдите собственную скорость теплохода

Answer 1

Обозначим скорость теплохода за х км/час, тогда его скорость по течению реки равна (Х+2,4), а против течения (х-2,4) км/час
1час 48 минут=1,8 час
1 час 30 минут=1,5 час
Уравнение
1,8*(х-2,4)=1,5(Х+2,4)
х=26,4 км/час

Answer 2

Problem Analysis

We are given that a boat traveled from point A to point B against the current and took 1 hour and 48 minutes. On the return journey from point B to point A, the boat took 18 minutes less. The speed of the river current is given as 2.4 km/h. We need to find the speed of the boat.

Solution

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

When the boat is traveling from point A to point B against the current, the effective speed of the boat is the difference between its speed and the speed of the current. So, the effective speed is (x - 2.4) km/h.

We are given that the boat took 1 hour and 48 minutes (or 1.8 hours) to travel from point A to point B. We can use the formula distance = speed × time to find the distance between point A and point B.

The distance from point A to point B is (x - 2.4) × 1.8 km.

On the return journey from point B to point A, the effective speed of the boat is the sum of its speed and the speed of the current. So, the effective speed is (x + 2.4) km/h.

We are given that the boat took 18 minutes (or 0.3 hours) less to travel from point B to point A. So, the time taken is 1.8 - 0.3 = 1.5 hours.

Using the formula distance = speed × time, we can find the distance from point B to point A, which is (x + 2.4) × 1.5 km.

Since the distance from point A to point B is the same as the distance from point B to point A, we can equate the two distances and solve for x.

Equation 1: (x - 2.4) × 1.8 = (x + 2.4) × 1.5

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

Calculation

Expanding Equation 1:

1.8x - 4.32 = 1.5x + 3.6

Rearranging the equation:

1.8x - 1.5x = 3.6 + 4.32

Simplifying:

0.3x = 7.92

Dividing both sides by 0.3:

x = 7.92 / 0.3

Calculating:

x = 26.4

Answer

The speed of the boat is 26.4 km/h.

Explanation

The boat traveled from point A to point B against the current at a speed of 26.4 km/h. On the return journey from point B to point A, the boat traveled at a speed of 26.4 km/h. The speed of the river current is 2.4 km/h. The boat took 1 hour and 48 minutes to travel from point A to point B and 18 minutes less to travel from point B to point A. By solving the equation, we found that the speed of the boat is 26.4 km/h.