Question

расстояние от пункта А до пункта В моторная лодка плыла по течению реки 1,3 ч,а от пункта В до пункта А-1,9 ч.Скорость течения реки 2,4 км/ч.Найдите собственную скорость моторной лодки

Answer 1

Problem Analysis

We are given the following information: - The motorboat traveled from point A to point B downstream in 1.3 hours. - The motorboat traveled from point B to point A upstream in 1.9 hours. - The speed of the river's current is 2.4 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 (from A to B), it is moving in the same direction as the current. In this case, the effective speed of the motorboat is the sum of its own speed and the speed of the current. Therefore, the equation for the downstream journey can be written as:

x + 2.4 = distance / 1.3 Similarly, when the motorboat is traveling upstream (from B to A), it is moving against the current. In this case, the effective speed of the motorboat is the difference between its own speed and the speed of the current. Therefore, the equation for the upstream journey can be written as:

x - 2.4 = distance / 1.9 To solve these equations, we need to find the distance between points A and B. Since the time taken for both journeys is different, we can assume that the distance between A and B is the same for both journeys.

Let's solve the equations to find the value of x.

Calculation

To find the distance, we can use the formula:

distance = speed × time

From equation we can rearrange it to find the distance:

distance = (x + 2.4) × 1.3 From equation we can rearrange it to find the distance:

distance = (x - 2.4) × 1.9 Since the distance is the same in both equations, we can equate them:

(x + 2.4) × 1.3 = (x - 2.4) × 1.9

Expanding and simplifying the equation:

1.3x + 3.12 = 1.9x - 4.56

0.6x = 7.68

x = 7.68 / 0.6

x = 12.8

Therefore, the speed of the motorboat is 12.8 km/h.

Answer

The speed of the motorboat is 12.8 km/h.

Explanation

The speed of the motorboat was calculated by considering the downstream and upstream journeys. By equating the distances traveled in both directions, we were able to solve for the speed of the motorboat. The calculations showed that the speed of the motorboat is 12.8 km/h.