Question

Задача: Лодка и плот одновременно двинулись по реке в одном направлении. Через три четверти часа расстояние между ними стало 450 м. С какой скоростью двигалась лодка, если плот двигался со скоростью 3 км/ч.? (Вырази скорость лодки в метрах в минуту.) Помогите, пожалуйста, с решением.

Answer 1

3/4 часа=45 мин
3км=3000м
1) 3000/60=50 (м/м)
2) 50*45=2250 (м)- расстояние,которое проплыл плот
3) 2250+450=2700 (м)-расстояние,которое проплыла лодка
5) 2700/45=60 (м/м)-скорость лодки
Ответ:лодка двигалась со скоростью 60м/м

Answer 2

Problem Analysis

We are given that a boat and a raft are moving in the same direction along a river. After three-quarters of an hour, the distance between them is 450 meters. We are also given that the raft is moving at a speed of 3 km/h. We need to determine the speed of the boat in meters per minute.

Solution

To solve this problem, we can use the formula: speed = distance / time.

Let's assume the speed of the boat is v meters per minute. Since the boat and the raft are moving in the same direction, the boat's effective speed relative to the river is the difference between the boat's speed and the raft's speed.

The distance covered by the boat in three-quarters of an hour is 3/4 * v meters, and the distance covered by the raft is 3/4 * 3 km/h.

According to the problem, the distance between the boat and the raft after three-quarters of an hour is 450 meters. We can set up the following equation:

3/4 * v - 3/4 * 3 km/h = 450 meters

Now, let's solve this equation to find the speed of the boat.

Calculation

To solve the equation, we need to convert the speed of the raft from km/h to meters per minute.

1 km/h = 1000 meters / 60 minutes = 16.67 meters per minute

Substituting the values into the equation:

3/4 * v - 3/4 * 16.67 meters/min = 450 meters

Simplifying the equation:

3/4 * v - 12.5 meters/min = 450 meters

Adding 12.5 meters/min to both sides of the equation:

3/4 * v = 450 meters + 12.5 meters/min

3/4 * v = 462.5 meters

Multiplying both sides of the equation by 4/3 to isolate v:

v = (462.5 meters) * (4/3)

v ≈ 616.67 meters per minute

Therefore, the speed of the boat is approximately 616.67 meters per minute.

Answer

The boat was moving at a speed of approximately 616.67 meters per minute.