Question

Помогите решить задачу с системами уравнений. Мне только решение)Лодка за 2 часа по течению и 5 часов против течения прошла 120 км.За 7 часов против течения лодка прошла на 52 км больше чем за 3 часа против течения.

Answer 1

Пусть скорость лодки в стоячей воде х, а скорость течения y
2(x+y)+5(x-y)=120  2(x+y)=120-5*(x-y) =120-5*13=55  x+y=27,5
7*(x-y)-52=3(x-y)  4*(x-y)=52  x-y=13
x-y=13
x+y=27,5
2x=40,5
x=20,25 скорость лодки
н=7,25 скорость течения

Answer 2

Пусть a = скорость лодки , b = скорость течения  , тогда блаблабла
$\left \{ {{ 2(a+b)+5(a-b)=120} \atop {7(a-b)-52=3(a-b)}} \right.$
Выразим например [a] из например первого уравнения и подставим во второе значение этого [a] .
2(a+b)+5(a-b)=120
2a+2b+5a-5b=120
7a-3b=120
a = (120+3b ) / 7
Подставляю во второе
7(a-b)-52=3(a-b)
7((120+3b ) / 7-b)-52=3((120+3b ) / 7-b)
Раскрой скобки
Найди b и подставь в a=(120+3b)/7

Answer 3

Problem Statement

We are given the following information about a boat's movement in a river: - The boat traveled 120 km in 2 hours downstream (with the current). - The boat traveled 120 km in 5 hours upstream (against the current). - The boat traveled 52 km more in 7 hours upstream than in 3 hours upstream.

We need to find the speed of the boat in still water and the speed of the current.

Solution

Let's assume the speed of the boat in still water is b km/h and the speed of the current is c km/h.

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

# Downstream Movement

When the boat is moving downstream, the effective speed is the sum of the boat's speed in still water and the speed of the current. Therefore, the distance traveled downstream can be calculated as: 120 km = (b + c) km/h × 2 hours.

# Upstream Movement

When the boat is moving upstream, the effective speed is the difference between the boat's speed in still water and the speed of the current. Therefore, the distance traveled upstream can be calculated as: 120 km = (b - c) km/h × 5 hours.

# Additional Information

According to the additional information given, the boat traveled 52 km more in 7 hours upstream than in 3 hours upstream. This can be expressed as: 52 km = (b - c) km/h × (7 hours - 3 hours).

Now, we have a system of equations that we can solve to find the values of b and c.

Let's solve the system of equations step by step.

# Step 1: Solve for b + c

From the equation for downstream movement, we have: 120 km = (b + c) km/h × 2 hours.

Simplifying the equation, we get: 2(b + c) = 120.

Dividing both sides by 2, we get: b + c = 60.

# Step 2: Solve for b - c

From the equation for upstream movement, we have: 120 km = (b - c) km/h × 5 hours.

Simplifying the equation, we get: 5(b - c) = 120.

Dividing both sides by 5, we get: b - c = 24.

# Step 3: Solve for b - c using the additional information

From the additional information, we have: 52 km = (b - c) km/h × (7 hours - 3 hours).

Simplifying the equation, we get: 4(b - c) = 52.

Dividing both sides by 4, we get: b - c = 13.

# Step 4: Solve the system of equations

We have two equations: 1. b + c = 60 2. b - c = 24

Adding equation 1 and equation 2, we get: 2b = 84.

Dividing both sides by 2, we get: b = 42.

Substituting the value of b into equation 1, we get: 42 + c = 60.

Subtracting 42 from both sides, we get: c = 18.

Therefore, the speed of the boat in still water is 42 km/h and the speed of the current is 18 km/h.

Answer

The speed of the boat in still water is 42 km/h and the speed of the current is 18 km/h.