Question

От двух пристаней расстояние между которыми 24 км одновременно в одном направлении отчалили лодка и катер ( лодок двигалась впереди катера). Скорость лодки равна 8 км/ч и составляет 4/5 скорость катера. Через сколько часов после начала движения катер догонит лодку?

Answer 1

Найдем скорость катера, обозначив через v. 4/5*v=8  v=8*5/4=10. Итак, скорость  катера 10 км/ч. Пусть у это количество часов, нужное для того чтобы катер догнал лодку, х - это общее расстояние до встречи. Составим уравнение 10у=х  8у=х-24 8у=10у-24 2у=24 у=12 Итак, они встретятся через 12 часов. Мжно ещё найти расстояние, подставив у в первое уравнение 10*12=х х=120 км

ПРосьба отметить как лучшее решение ))

Answer 2

8:4/5=8*5/4=10км/ч скорость катера
10-8=2км/ч скорость сближения катера
24:2=12ч-время через которое катер догонит лодку

Answer 3

Problem Analysis

We are given that the distance between two piers is 24 km. A boat and a motorboat simultaneously depart from the piers in the same direction, with the boat ahead of the motorboat. The speed of the boat is 8 km/h, which is 4/5 of the speed of the motorboat. We need to determine how many hours it will take for the motorboat to catch up to the boat.

Solution

Let's assume that the speed of the motorboat is x km/h. According to the problem, the speed of the boat is 4/5 of the speed of the motorboat, so the speed of the boat is (4/5)x km/h.

We can use the formula: distance = speed × time to solve this problem.

Let's denote the time it takes for the motorboat to catch up to the boat as t hours.

The distance traveled by the motorboat in t hours is given by: distance_motorboat = x × t km.

The distance traveled by the boat in t hours is given by: distance_boat = (4/5)x × t km.

Since the boat is ahead of the motorboat, the distance traveled by the boat is equal to the distance between the piers, which is 24 km.

Therefore, we can set up the equation: (4/5)x × t = 24.

To find the value of t, we need to solve this equation for x.

Calculation

Let's solve the equation (4/5)x × t = 24 for t.

(4/5)x × t = 24

Multiplying both sides of the equation by 5/4 to isolate t, we get:

t = (24 × 5/4) / (4/5)

Simplifying the expression, we get:

t = 30 / 4

t = 7.5

Therefore, it will take 7.5 hours for the motorboat to catch up to the boat.

Answer

After 7.5 hours of starting their journey, the motorboat will catch up to the boat.

Note: The answer is rounded to one decimal place.