Question

Две моторные лодки движутся вдоль направления течения реки навстречу друг другу. Скорость течения реки 2 м/с, скорость каждой лодки относительно воды 3 м/с. Через сколько времени после встречи лодок расстояние между ними станет равным 120 м?

Answer 1

120/ (2+3 + 3-2)=20 с - искомое время

Answer 2

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Answer 3

Problem Analysis

Two motorboats are moving along the direction of the river's current towards each other. The river's current speed is 2 m/s, and the speed of each boat relative to the water is 3 m/s. We need to determine the time it takes for the distance between the boats to become 120 m after they meet.

Solution

To solve this problem, we can use the concept of relative motion. When the boats meet, the distance between them will be the sum of the distances traveled by both boats. We can calculate the time it takes for the boats to cover this distance.

Let's denote: - Speed of the river's current = 2 m/s - Speed of each boat relative to the water = 3 m/s - Distance between the boats when they meet = 120 m

When the boats meet, the distance covered by Boat 1 + the distance covered by Boat 2 = 120 m.

Calculations

The time it takes for the boats to cover the distance can be calculated using the formula: \[ \text{Time} = \frac{\text{Distance}}{\text{Relative Speed}} \]

The relative speed of the boats is the sum of their speeds relative to the water, as they are moving towards each other.

Let's calculate the time it takes for the boats to cover the distance.

Time Calculation

The relative speed of the boats: \[ \text{Relative Speed} = \text{Speed of Boat 1} + \text{Speed of Boat 2} \]

\[ \text{Relative Speed} = 3 \, \text{m/s} + 3 \, \text{m/s} = 6 \, \text{m/s} \]

Now, we can calculate the time it takes for the boats to cover the distance: \[ \text{Time} = \frac{120 \, \text{m}}{6 \, \text{m/s}} = 20 \, \text{s} \]

Answer

After the boats meet, the distance between them will become 120 m after 20 seconds.