Question

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

Answer 1

99/22=4(раза)лодка быстрее.2.22*4=88(км/ч)-скорость лодки по течению реки.3.88-2=86(км/ч) собственная скорость лодки. Ответ:86(км/ч)

Answer 2

Problem Analysis

We are given that the distance between two ports, A and B, is 99 km. A raft starts from A and after an hour, a motorboat starts from A and reaches B. The motorboat immediately turns back and returns to A. By the time the motorboat reaches 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. Since the motorboat travels with the current while going from A to B, its effective speed is (x + 2) km/h. On the return journey from B to A, the motorboat travels against the current, so its effective speed is (x - 2) km/h.

We can calculate the time taken by the motorboat to travel from A to B using the formula:

Time = Distance / Speed

The time taken by the motorboat to travel from B to A is the same as the time taken to travel from A to B. Therefore, the total time taken by the motorboat for the round trip is:

Total Time = Time (A to B) + Time (B to A)

Since the raft travels at a constant speed, we can calculate the time taken by the raft to travel from A to the point where the motorboat turns back using the formula:

Time (A to turning point) = Distance / Speed

Given that the raft has traveled 22 km by the time the motorboat reaches B, we can calculate the remaining distance traveled by the raft:

Distance (A to turning point) = Total Distance - Distance (A to B)

Now, we can calculate the time taken by the raft to travel from the turning point to B:

Time (turning point to B) = Distance (A to turning point) / Speed

Since the total time taken by the motorboat for the round trip is equal to the sum of the time taken by the motorboat and the time taken by the raft, we can write the equation:

Total Time = Time (A to B) + Time (B to A) = Time (A to B) + Time (turning point to B)

We can substitute the values and solve for x, the speed of the motorboat in still water.

Calculation

Let's calculate the speed of the motorboat in still water.

Given: - Distance between A and B = 99 km - Speed of the river current = 2 km/h - Distance traveled by the raft = 22 km

First, let's calculate the time taken by the motorboat to travel from A to B:

Time (A to B) = Distance (A to B) / Speed (A to B)

Time (A to B) = 99 km / (x + 2) km/h

Next, let's calculate the distance traveled by the raft from the turning point to B:

Distance (turning point to B) = Total Distance - Distance (A to B)

Distance (turning point to B) = 99 km - 22 km = 77 km

Now, let's calculate the time taken by the raft to travel from the turning point to B:

Time (turning point to B) = Distance (turning point to B) / Speed (raft)

Time (turning point to B) = 77 km / 2 km/h = 38.5 h

Since the total time taken by the motorboat for the round trip is equal to the sum of the time taken by the motorboat and the time taken by the raft, we can write the equation:

Total Time = Time (A to B) + Time (B to A) = Time (A to B) + Time (turning point to B)

Total Time = 1 h + 1 h = 2 h

Now, let's substitute the values and solve for x:

2 h = 99 km / (x + 2) km/h + 38.5 h

Simplifying the equation:

2 h - 38.5 h = 99 km / (x + 2) km/h

-36.5 h = 99 km / (x + 2) km/h

Cross-multiplying:

-36.5 h * (x + 2) km/h = 99 km

-36.5x - 73 km/h = 99 km

-36.5x = 99 km + 73 km

-36.5x = 172 km

Dividing both sides by -36.5:

x = -172 km / -36.5

x = 4.71 km/h

Therefore, the speed of the motorboat in still water is approximately 4.71 km/h.

Answer

The speed of the motorboat in still water is approximately 4.71 km/h.