Question

Расстояние между двумя пунктами катер прошёл по течению реки за 7 часов, а против течения - за 8 часов. Найдите расстояние между этими пунктами если скорость течения реки 3,5 км/ч.

Answer 1

Х собственная скорость
х+3,5 скорость по течению
х-3,5 против течения
8(х-3,5)=7(х+3,5)
8х-28=7х+24,5
х=52,5км/час собственная скорость

Answer 2

пусть скорость катера равна х

переведем часы в десятичный вид и составим уравнение

(х+2,4)*3,5=(х-2,4)*6,3

3,5х+8,4=6,3х-15,12

15,12+8,4=6,3х-3,5х

2,8х=23,52

х=8,4

расстояние равно (8,4+2,4)*3,5=37,8 км

Answer 3

Problem Analysis

We are given that a boat traveled between two points along a river. It took 7 hours to travel downstream with the current and 8 hours to travel upstream against the current. We need to find the distance between these two points, given that the speed of the river's current is 3.5 km/h.

Downstream Travel

When the boat is traveling downstream, it benefits from the speed of the river's current. Let's assume the speed of the boat in still water is x km/h. The effective speed of the boat when traveling downstream is the sum of its speed in still water and the speed of the current, which is x + 3.5 km/h.

We are given that the boat took 7 hours to travel downstream. The distance traveled can be calculated by multiplying the effective speed by the time taken: distance = speed × time.

Upstream Travel

When the boat is traveling upstream, it has to overcome the speed of the river's current. In this case, the effective speed of the boat is the difference between its speed in still water and the speed of the current, which is x - 3.5 km/h.

We are given that the boat took 8 hours to travel upstream. Again, the distance traveled can be calculated by multiplying the effective speed by the time taken: distance = speed × time.

Solution

To find the distance between the two points, we can equate the distances traveled downstream and upstream. Let's denote the distance between the two points as d km.

Using the formulas derived above, we can set up the following equation:

d = (x + 3.5) × 7 (downstream distance)

d = (x - 3.5) × 8 (upstream distance)

We can solve this system of equations to find the value of d.

Calculation

Let's solve the system of equations to find the distance d.

d = (x + 3.5) × 7

d = (x - 3.5) × 8

Expanding the equations:

7x + 24.5 = 8x - 28

Rearranging the equation:

x = 52.5

Substituting the value of x back into one of the equations:

d = (52.5 + 3.5) × 7

d = 56 × 7

d = 392 km

Answer

The distance between the two points is 392 km.