Question

По течению реки движутся катер и плот. Через некоторое время они поравнялись, а ещё через минуту расстояние между ними составило 600 м. Катер прибыл в пункт назначения через 30 минут, а плот - через 5,5 часа. Считая движение плота и катера равномерным и прямолинейным, определить скорость воды в реке.

Answer 1

1)
Поскольку за 1 минуту катер проходит расстояние 600 метров, то расстояние за 30 минут :
S = 600*30 = 18 000 м      или  18 км
Значит, скорость катера (собственная+скорость реки)
V = 36 км/ч

2)
Пусть скорость реки равна X, тогда составим пропорцию:
36 / X = 5,5 / 0,5
36 / X = 5
X = 36/5 ≈ 7 км/ч

Answer 2

Problem Analysis

We are given that a boat and a raft are moving in a river. After a certain time, they are level with each other, and a minute later, the distance between them is 600 meters. The boat reaches its destination in 30 minutes, while the raft takes 5.5 hours. We need to determine the speed of the water in the river.

Solution

Let's assume the speed of the boat is v_boat and the speed of the raft is v_raft. The speed of the water in the river is denoted as v_water.

We can start by analyzing the boat's and raft's movements separately.

Boat's Movement

The boat reaches its destination in 30 minutes, so we can calculate its speed using the formula:

Speed = Distance / Time

The distance traveled by the boat is equal to the distance between the boat and the raft when they were level, plus the additional distance they covered in 30 minutes. Let's denote this distance as d_boat.

d_boat = 600 meters + v_raft * 30 minutes

Now we can calculate the speed of the boat:

v_boat = d_boat / 30 minutes

Raft's Movement

The raft takes 5.5 hours to reach its destination. Let's denote the distance traveled by the raft as d_raft.

d_raft = v_raft * 5.5 hours

Relationship between Boat's and Raft's Speeds

When the boat and the raft were level, they covered the same distance. Let's denote this distance as d_level.

d_level = d_boat = d_raft

Using the above equations, we can write:

600 meters + v_raft * 30 minutes = v_raft * 5.5 hours

Now we need to convert the units to be consistent. Let's convert 30 minutes to hours:

30 minutes = 30 / 60 hours = 0.5 hours

Substituting the values:

600 meters + v_raft * 0.5 hours = v_raft * 5.5 hours

Simplifying the equation:

600 meters = v_raft * 5 hours

Now we can solve for v_raft:

v_raft = 600 meters / 5 hours

Calculating the Speed of the Water

The speed of the water in the river is equal to the difference between the speed of the boat and the speed of the raft:

v_water = v_boat - v_raft

Substituting the values:

v_water = (d_boat / 30 minutes) - (600 meters / 5 hours)

Now we need to convert the units to be consistent. Let's convert 30 minutes to hours:

30 minutes = 30 / 60 hours = 0.5 hours

Substituting the values:

v_water = (d_boat / 0.5 hours) - (600 meters / 5 hours)

Simplifying the equation:

v_water = (2 * d_boat - 600 meters) / 5 hours

Now we can calculate the speed of the water in the river.

Calculation

Let's calculate the speed of the water in the river using the given information.

d_boat = 600 meters + v_raft * 30 minutes

v_boat = d_boat / 30 minutes

d_raft = v_raft * 5.5 hours

600 meters + v_raft * 0.5 hours = v_raft * 5.5 hours

v_raft = 600 meters / 5 hours

v_water = (2 * d_boat - 600 meters) / 5 hours

Now we can substitute the values and calculate the speed of the water in the river.