Question

першого дня Катер проплив 3 години за течією річки та дві години проти течії подолав 112 км. Другого дня він проплив 4 години за течією і одну годину проти течії подолавши 126 км знайти швидкість течії ріки​

Answer 1

Ответ:

7 км/ч

Пошаговое объяснение:

Скорость катера по течению = х км/ч

Скорость катера против течения = у км/ч

3х + 2у = 112

4х + у = 126 | * -2

3х + 2у = 112

-8х - 2у = -252

-5х = -140

3х + 2у = 112

1)

-5х = -140

х = -140 : -5

х = 28

2)

3х + 2у = 112

3*28 + 2у = 112

84 + 2у = 112

2у = 112 - 84

2у = 28

у = 28 : 2

у = 14

Скорость катера по течению = (х) = 28 км/ч

Скорость катера против течения = (у) = 14 км/ч

(28 - 14) : 2 = 14 : 2 = 7 км/ч - скорость течения реки

Answer 2

Problem Analysis

To find the speed of the river current, we need to set up a system of equations based on the given information. Let's assume the speed of the boat in still water is b and the speed of the river current is c.

Solution

Let's analyze the information given for the first day: - The boat traveled downstream (with the current) for 3 hours and covered a distance of 112 km. - The boat traveled upstream (against the current) for 2 hours and covered the same distance of 112 km.

Using the formula distance = speed × time, we can set up the following equations: 1. For downstream travel: (b + c) × 3 = 112 2. For upstream travel: (b - c) × 2 = 112

Now, let's analyze the information given for the second day: - The boat traveled downstream (with the current) for 4 hours and covered a distance of 126 km. - The boat traveled upstream (against the current) for 1 hour and covered the same distance of 126 km.

Using the same formula, we can set up the following equations: 3. For downstream travel: (b + c) × 4 = 126 4. For upstream travel: (b - c) × 1 = 126

We now have a system of four equations with two variables (b and c). We can solve this system of equations to find the values of b and c.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation 2, we can express b in terms of c: (b - c) × 2 = 112 Simplifying, we get: b - c = 56 So, we have b = c + 56.

Now, let's substitute this value of b in equation 1: (b + c) × 3 = 112 Substituting b = c + 56, we get: (c + 56 + c) × 3 = 112 Simplifying, we get: 2c + 56 = 112 Subtracting 56 from both sides, we get: 2c = 56 Dividing both sides by 2, we get: c = 28

Therefore, the speed of the river current is 28 km/h.

Conclusion

The speed of the river current is 28 km/h.