Question

За 2 часа катер проходит по течению реки расстояние1.25 раза меньшее чем за 3 часа против течения. какова скопость катера в стоячей воде,если скорость течения1,5 км/ч

Answer 1

Пусть х км/ч - собственная скорость катера, тогда (х + 1,5) км/ч - скорость катера по течению реки, (х - 1,5) км/ч - скорость катера против течения реки. За 2 часа катер пройдёт по течению 2 * (х + 1,5) км, за 3 часа против течения 3 * (х - 1,5) км. Расстояние по течению в 1,25 раза меньше расстояния против течения. Уравнение:
1,25 * 2 * (х + 1,5) = 3 * (х - 1,5)
2,5х + 3,75 = 3х - 4,5
3,75 + 4,5 = 3х - 2,5х
8,25 = 0,5х
х = 8,25 : 0,5
х = 16,5 (км/ч) - собственная скорость катера 
Ответ: 16,5 км/ч скорость катера в стоячей воде.

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the boat in still water. We are given that the boat takes 2 hours to travel a certain distance downstream (with the current) and 3 hours to travel the same distance upstream (against the current). We are also given that the current speed is 1.5 km/h.

Let's assume the speed of the boat in still water is x km/h and the distance traveled is d km.

Downstream Speed

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. Therefore, the downstream speed is (x + 1.5) km/h.

Using the formula speed = distance / time, we can write the equation: (x + 1.5) = d / 2 (since the boat takes 2 hours to travel the distance downstream)

Upstream Speed

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. Therefore, the upstream speed is (x - 1.5) km/h.

Using the same formula, we can write the equation: (x - 1.5) = d / 3 (since the boat takes 3 hours to travel the distance upstream)

Solving the Equations

We now have a system of two equations with two unknowns (x and d). We can solve this system to find the values.

Let's solve the equations:

From the first equation, we can express d in terms of x: d = 2(x + 1.5)

Substituting this value of d into the second equation: (x - 1.5) = (2(x + 1.5)) / 3

Simplifying the equation: 3(x - 1.5) = 2(x + 1.5) 3x - 4.5 = 2x + 3 x = 7.5

Answer

The speed of the boat in still water is 7.5 km/h.

Explanation

When the boat is traveling downstream, its speed is the sum of its speed in still water and the speed of the current. Therefore, the downstream speed is (7.5 + 1.5) = 9 km/h.

When the boat is traveling upstream, its speed is the difference between its speed in still water and the speed of the current. Therefore, the upstream speed is (7.5 - 1.5) = 6 km/h.

Please let me know if you need any further clarification or assistance!