Question

теплоход прошёл расстояние между пристанями по течению реки за 4 ч,а против течения реки за 5 ч.Определите собственную скорость теплохода,если скорость течения реки 2км\ч.Каково расстояние между приятанями?(Сделайте пожалуйста схемку..ну чертёж как бы и желательно во вложениях)решите через х

Answer 1

Х км/ч  -  собственная скорость теплохода
(х + 2) км/ч  -  скорость по течению
(х - 2) км/ч  -  скорость против течения

1) (х + 2) * 4 = (х - 2) * 5
    4х + 8 = 5х - 10
    4х - 5х = - 10 - 8
   - х = - 18
    х = 18 км/ч - собственная скорость теплохода
2) (18 + 2) * 4 = 20 * 4 = 80 км - расстояние между пристанями
или :
    (18 - 2) * 5 = 16 * 5 = 80 км - расстояние.

Answer 2

Problem Analysis

We are given that a boat traveled a certain distance between two docks along a river. The boat traveled downstream (with the current) in 4 hours and upstream (against the current) in 5 hours. We are also given that the speed of the river's current is 2 km/h. We need to determine the speed of the boat and the distance between the docks.

Solution

Let's assume the speed of the boat is x km/h.

When the boat is traveling downstream (with the current), its effective speed is the sum of its own speed and the speed of the current. Therefore, the effective speed is (x + 2) km/h.

When the boat is traveling upstream (against the current), its effective speed is the difference between its own speed and the speed of the current. Therefore, the effective speed is (x - 2) km/h.

We can use the formula distance = speed × time to calculate the distance traveled in each case.

1. Downstream: - Speed = (x + 2) km/h - Time = 4 hours - Distance = (x + 2) × 4 km

2. Upstream: - Speed = (x - 2) km/h - Time = 5 hours - Distance = (x - 2) × 5 km

Since the distance between the docks is the same in both cases, we can equate the two distances and solve for x:

(x + 2) × 4 = (x - 2) × 5

Let's solve this equation to find the value of x:

4x + 8 = 5x - 10 8 + 10 = 5x - 4x 18 = x

Therefore, the speed of the boat is 18 km/h.

To find the distance between the docks, we can substitute the value of x into either of the distance formulas:

Distance = (x + 2) × 4 = (18 + 2) × 4 = 20 × 4 = 80 km

Therefore, the distance between the docks is 80 km.

Diagram

Here's a diagram to help visualize the problem:

``` Dock A ----------------------> Dock B | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |