Question

Плот и лодка движутся навстречу друг другу по реке. Они находятся на расстоянии 32 км друг от друга. Через какое время они встретятся если собственная скорость лодки 10 км в ч, а скорость течения реки 3 км в ч.

Answer 1

Так как лодка и плот движутся навстречу, то плот плывет по течению, а лодка - против течения.

Скорость течения реки v₀ = 3 км/ч
Скорость лодки v₂ = 10 (км/ч)
Скорость плота v₁ = v₀ = 3 км/ч

Скорость сближения лодки и плота: v = v₁ + v₂ = v₀ + (v₂ - v₀) = v₂

Время до их встречи: t = S/v₂ = 32/10 = 3,2 = 3 ч 12 мин

Ответ: через 3 ч 12 мин

Answer 2

Problem Analysis

We are given that a boat and a raft are moving towards each other on a river. The distance between them is 32 km. The boat's speed is 10 km/h, and the river's current speed is 3 km/h. We need to find out how long it will take for them to meet.

Solution

To solve this problem, we can use the concept of relative velocity. The relative velocity is the difference between the velocities of two objects. In this case, we need to find the relative velocity between the boat and the raft.

The velocity of the boat with respect to the ground is 10 km/h, and the velocity of the river current is 3 km/h. Since the boat is moving against the current, we subtract the velocity of the current from the boat's velocity to get the relative velocity of the boat with respect to the ground:

Relative velocity of the boat = Boat's velocity - River current's velocity = 10 km/h - 3 km/h = 7 km/h

Now, we can calculate the time it will take for the boat and the raft to meet by dividing the distance between them by the relative velocity:

Time = Distance / Relative velocity = 32 km / 7 km/h

Let's calculate the time:

Time = 32 km / 7 km/h = 4.57 hours

Therefore, it will take approximately 4.57 hours for the boat and the raft to meet.

Answer

The boat and the raft will meet in approximately 4.57 hours.

Explanation

When two objects are moving towards each other, the time taken to meet can be calculated by dividing the distance between them by the relative velocity. In this case, the relative velocity is the difference between the boat's velocity and the river current's velocity. By substituting the given values into the formula, we find that it will take approximately 4.57 hours for the boat and the raft to meet.