Question

Катер движется по реке, скорость течения 3км/ч. Расстояние между пристанями составляет 100 км. При движении по течению реки катер проходит это расстояние менее, чем за 4 ч, а при движении против течения - более, чем за 5 ч.Какова собственная скорость катера?

Answer 1

Пусть собственная скорость катера - х.   ⇒
100/(x+3)<4   100<4+12     4x>88          x>22
100/(x-3)>5    100>5x-15    5x<115        x<23   ⇒
x∈(22;23)
Ответ: скорость катера от 22 км/ч до 23 км/ч.

Answer 2

Calculation of the Boat's Speed

To calculate the boat's speed, we need to consider the speed of the current and the time it takes for the boat to travel between the two piers in different directions.

Let's denote the boat's speed as x km/h and the speed of the current as 3 km/h.

When the boat is moving downstream (with the current), it takes less than 4 hours to cover the distance of 100 km. On the other hand, when the boat is moving upstream (against the current), it takes more than 5 hours to cover the same distance.

To find the boat's speed, we can set up the following equations:

1. When moving downstream: - Time taken = Distance / (Boat's speed + Current's speed) - 100 / (x + 3) < 4

2. When moving upstream: - Time taken = Distance / (Boat's speed - Current's speed) - 100 / (x - 3) > 5

Let's solve these equations to find the boat's speed.

Solving the Equations

1. When moving downstream: - 100 / (x + 3) < 4 - 100 < 4(x + 3) - 100 < 4x + 12 - 88 < 4x - x > 22

2. When moving upstream: - 100 / (x - 3) > 5 - 100 > 5(x - 3) - 100 > 5x - 15 - 115 > 5x - x < 23

From the above equations, we can conclude that the boat's speed (x) is greater than 22 km/h and less than 23 km/h.

Therefore, the boat's speed is between 22 km/h and 23 km/h.

Please note that the exact value of the boat's speed cannot be determined without additional information.