Question

№4 Від двох пристаней, відстань між якими 51 км, назустріч один одному рухаються два моторні човни, власна швидкість кожного 15 км/год. До зустрічі човен, що йде за течією річки, рухається 1,5 год, а човен, що йде проти течії, — 2 год. Знайдіть швидкість течії річки.​

Answer 1

Ответ:

Пошаговое объяснение:

скорость течеия реки х км/час

скорость по течению (15+х) км/час и путь по течению (15+х)*1,5 км

скорость против течения (15-х) км/час и путь против  течения (15+х)*2 км

и тогда уравнение

1,5(15+х) = 2(15-х)

22,5 +1,5х = 30 -2 х

2,5х = 7,5

х = 3

ответ

швидкість течії річки 3 км/час

Answer 2

Problem Analysis

We are given two motorboats moving towards each other on a river. The distance between the two ports is 51 km, and the speed of each boat is 15 km/h. We are also given the time it takes for the boat moving downstream to reach the meeting point and the time it takes for the boat moving upstream to reach the meeting point. We need to find the speed of the river's current.

Solution

Let's assume the speed of the river's current is x km/h.

When the boat is moving downstream, it gets assistance from the current, so its effective speed is the sum of its own speed and the speed of the current. Therefore, the effective speed of the boat moving downstream is (15 + x) km/h.

When the boat is moving upstream, it has to overcome the current, so its effective speed is the difference between its own speed and the speed of the current. Therefore, the effective speed of the boat moving upstream is (15 - x) km/h.

We can use the formula speed = distance / time to find the distance traveled by each boat.

For the boat moving downstream, the distance traveled is (15 + x) * 1.5 km (since it takes 1.5 hours to reach the meeting point).

For the boat moving upstream, the distance traveled is (15 - x) * 2 km (since it takes 2 hours to reach the meeting point).

Since the two boats are moving towards each other, the sum of the distances traveled by each boat should be equal to the total distance between the ports, which is 51 km.

Therefore, we can write the equation:

(15 + x) * 1.5 + (15 - x) * 2 = 51

Simplifying the equation:

22.5 + 1.5x + 30 - 2x = 51

Combining like terms:

-0.5x + 52.5 = 51

Subtracting 52.5 from both sides:

-0.5x = -1.5

Dividing both sides by -0.5:

x = 3

Therefore, the speed of the river's current is 3 km/h.

Answer

The speed of the river's current is 3 km/h.