Question

Расстояние между пристанями A и B равно 99 км. Из A в B по течению реки отправился плот, а через час вслед за ним отправилась моторная лодка, которая, прибыв в пункт B тотчас повернула обратно и возвратилась в A. К этому времени плот прошел 22 км. Найдите скорость лодки в неподвижной воде, если скорость течения реки равна 2 км/ч.

Answer 1

Решение смотри во вложении:

Answer 2

Problem Analysis

We are given that the distance between two docks, A and B, is 99 km. A raft starts from dock A and after an hour, a motorboat starts from dock A and travels towards dock B. Upon reaching dock B, the motorboat immediately turns back and returns to dock A. By the time the motorboat reaches dock B, the raft has traveled 22 km. We need to find the speed of the motorboat in still water, given that the speed of the river current is 2 km/h.

Solution

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

The speed of the motorboat relative to the river current is the difference between the speed of the motorboat in still water and the speed of the river current. Therefore, the speed of the motorboat relative to the river current is (x - 2) km/h.

Since the motorboat travels 22 km in the same time it takes the raft to travel the remaining distance of 99 - 22 = 77 km, we can set up the following equation:

22 / (x - 2) = 77 / x

To solve for x, we can cross-multiply and solve the resulting equation.

Calculation

Cross-multiplying the equation, we get:

22x = 77(x - 2)

Expanding the equation:

22x = 77x - 154

Simplifying the equation:

55x = 154

Solving for x:

x = 154 / 55

Evaluating the expression:

x ≈ 2.8

Answer

The speed of the motorboat in still water is approximately 2.8 km/h.

Explanation

The speed of the motorboat in still water is found by solving the equation 22 / (x - 2) = 77 / x. By cross-multiplying and simplifying, we find that x ≈ 2.8. This means that the motorboat can travel at a speed of approximately 2.8 km/h in still water.