Question

Баржа в 10:00 вышла из пункта А в пункт В, расположенный в 15 км от А. Пробыв в пункте В 1 час 20 минут, баржа отправилась назад и вернулась в пункт А в 16:00. Определите (в км/час) скорость течения реки, если известно, что собственная скорость баржи равна 7 км/ч.

Answer 1

Пусть скорость течения реки х, тогда скорость баржи по течению реки равна 7+х, а против течения 7-х. По течению реки баржа шла $\frac{15}{x+7}$ часов, а против течения $\frac{15}{7-x}$. Общее время баржи в пути 16-10-1$\frac{1}{3}$=$\frac{14}{3}$.

По условию задачи составим уравнение

$\frac{15x}{x+7}+\frac{15}{7-x}=\frac{14}{3}$$\frac{15x+105+105-15x}{(x+7)(7-x)}=\frac{14}{3}$   $14(x+7)(7-x)=630$    $49-x^{2}=45$     $x^{2}=4$    $x=2$

Ответ: скорость течения реки 2 км/ч

 

 

 

 

 

 

 

 

 

 

Answer 2

Problem Analysis

We are given that a barge left point A at 10:00 and traveled to point B, which is located 15 km away from A. The barge stayed at point B for 1 hour and 20 minutes before returning to point A at 16:00. We need to determine the speed of the river current if the barge's own speed is 7 km/h.

Solution

To solve this problem, we can use the formula: distance = speed x time.

Let's denote the speed of the river current as x km/h. The barge's speed is given as 7 km/h.

# Distance from A to B

The distance from A to B is given as 15 km.

# Time from A to B

The time taken by the barge to travel from A to B is not explicitly given. However, we can calculate it using the formula distance = speed x time.

Let's denote the time taken from A to B as t1.

Using the formula, we have: 15 km = (7 km/h + x km/h) x t1

Simplifying the equation, we get: 15 = (7 + x) x t1

# Time from B to A

The time taken by the barge to travel from B to A is given as 1 hour and 20 minutes, which is equivalent to 1.33 hours.

Let's denote the time taken from B to A as t2.

Using the formula, we have: 15 km = (7 km/h - x km/h) x t2

Simplifying the equation, we get: 15 = (7 - x) x t2

# Total Time

The total time taken for the round trip is given as 6 hours (from 10:00 to 16:00).

Let's denote the total time as t.

Using the formula, we have: t = t1 + t2

Substituting the values, we get: 6 = t1 + 1.33

Simplifying the equation, we get: t1 = 6 - 1.33 t1 = 4.67 hours

# Solving the Equations

Now, we have two equations: 1. 15 = (7 + x) x t1 2. 15 = (7 - x) x t2

Substituting the values of t1 and t2, we get: 1. 15 = (7 + x) x 4.67 2. 15 = (7 - x) x 1.33

Simplifying the equations, we get: 1. 15 = 32.69 + 4.67x 2. 15 = 9.31 - 1.33x

Rearranging the equations, we get: 1. 4.67x = 15 - 32.69 2. 1.33x = 15 - 9.31

Simplifying further, we get: 1. 4.67x = -17.69 2. 1.33x = 5.69

Solving for x, we get: 1. x = -17.69 / 4.67 2. x = 5.69 / 1.33

Calculating the values, we get: 1. x ≈ -3.78 km/h 2. x ≈ 4.28 km/h

Since the speed of the river current cannot be negative, we can conclude that the speed of the river current is approximately 4.28 km/h.

Answer

The speed of the river current is approximately 4.28 km/h.