Question

помогите решить задачу пожалуйста Моторная лодка шла 40 мин по течению реки и 1 час 30 минут против.За все это время она прошла 41.4 км. Чему равна скорость течения реки, если скорость лодки по течению на 20%больше ее скорости против течения??

Answer 1

V - скорость

S - расстояние

_____________________ 

х км/ч - скорость лодки

1,2*х - скорость по течению

0,8 - против течения

S = 2/3*(1,2*х) + 1,5*(0,8*х)

х = 20,7

V (т-ия) = 20,7*0,2 = 4,14 км/ч

Answer 2

Problem Analysis

To solve this problem, we need to find the speed of the river current. We are given that a motorboat traveled for 40 minutes with the current and 1 hour 30 minutes against the current, covering a total distance of 41.4 km. Additionally, we are told that the speed of the boat with the current is 20% greater than its speed against the current.

Solution

Let's denote the speed of the boat in still water as x km/h and the speed of the river current as y km/h.

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

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

We are given that the boat traveled for 40 minutes (or 2/3 hours) with the current and 1 hour 30 minutes (or 1.5 hours) against the current, covering a total distance of 41.4 km.

Using the formula distance = speed × time, we can set up the following equations:

Equation 1: (x + y) × (2/3) = 41.4 (when traveling with the current) Equation 2: (x - y) × (1.5) = 41.4 (when traveling against the current)

We can solve this system of equations to find the values of x and y.

Solving the Equations

Let's solve Equation 1 for x + y:

(x + y) × (2/3) = 41.4

Multiplying both sides by 3/2:

x + y = 41.4 × (3/2) x + y = 62.1 (Equation 3)

Now, let's solve Equation 2 for x - y:

(x - y) × (1.5) = 41.4

Multiplying both sides by 2/3:

x - y = 41.4 × (2/3) x - y = 27.6 (Equation 4)

We now have a system of equations with two variables (x and y):

Equation 3: x + y = 62.1 Equation 4: x - y = 27.6

To solve this system, we can add Equation 3 and Equation 4:

(x + y) + (x - y) = 62.1 + 27.6

Simplifying:

2x = 89.7

Dividing both sides by 2:

x = 44.85

Now, we can substitute the value of x back into Equation 3 to find y:

44.85 + y = 62.1

Simplifying:

y = 62.1 - 44.85 y = 17.25

Answer

Therefore, the speed of the river current is 17.25 km/h.

Please note that the values of x and y have been rounded to two decimal places for simplicity.

Let me know if you need any further assistance!