Question

В 19 часов от двух пристаней, расстояние между которыми 3 км, одновременно в одном направлении отошли два быстроходных катера. Скорость одного из них была 48 км/ч, а другой догонял его со скоростью 54 км/ч. В котором часу второй катер догонит первый? (необходимо выразить скорости катеров в метрах в минуту, а расстояние - в метрах).

Answer 1

54-48=6км/ч - скорость одного катера больше другого 3км:6км/час 3000м:6000м/60мин=3000м:100м/мин=30мин надо времени, чтобы догнать катер 19ч+30мин=19часов30мин Ответ в 19ч30мин

Answer 2

Problem Analysis

We have two fast boats that start simultaneously from two different piers, with a distance of 3 km between them. One boat has a speed of 48 km/h, while the other boat is chasing it at a speed of 54 km/h. We need to determine at what time the second boat will catch up to the first boat. To solve this problem, we need to convert the speeds of the boats to meters per minute and the distance between the piers to meters.

Conversion of Units

To convert the speeds of the boats from km/h to m/min, we can use the following conversion factors: - 1 km = 1000 m - 1 h = 60 min

Therefore, the speed of the first boat in m/min is: 48 km/h * (1000 m/km) * (1 h/60 min) = 800 m/min

And the speed of the second boat in m/min is: 54 km/h * (1000 m/km) * (1 h/60 min) = 900 m/min

To convert the distance between the piers from km to meters, we multiply by 1000: 3 km * 1000 m/km = 3000 m

Calculation

Now that we have the speeds of the boats in m/min and the distance between the piers in meters, we can calculate the time it takes for the second boat to catch up to the first boat.

Let's assume that the time it takes for the second boat to catch up to the first boat is t minutes.

During this time, the first boat will travel a distance of 800t meters, and the second boat will travel a distance of 900t meters.

Since the second boat is chasing the first boat, the distance traveled by the second boat will be equal to the distance between the piers.

Therefore, we can set up the following equation: 800t + 900t = 3000

Simplifying the equation: 1700t = 3000

Solving for t: t = 3000 / 1700 ≈ 1.765 minutes

Answer

Therefore, the second boat will catch up to the first boat approximately 1.765 minutes after they start.

Note: The exact time can be calculated by converting the decimal part of the minutes to seconds and adding it to the whole number of minutes. However, since the question does not specify the level of precision required, we have provided the answer rounded to three decimal places.

Please let me know if you need any further assistance!