Question

Катер прошел 18 км вверх по течению и 14 км вниз по течению. Это путешествие занимает 3 часа 15 минут. Скорость катера 10 км/ч. Найдите скорость потока ​

Answer 1

Ответ:

0.77 км/ч

Объяснение:

t1 = 18 / (10 - x) время затраченное против течения

t2 = 14 / (10 + x) время затраченное по течению

t1 + t2 = 3.25 часа

18 / (10 - x) + 14 / (10 + x) = 3.25

умножаем все на (10 - x)(10 + x):

18 * (10 + x) + 14 * (10 - x) = 3.25 * (100 - x²)

180 + 18x + 140 - 14x = 325 - 3.25x²

3.25x² + 4x - 5 = 0

13x² + 16x - 20 = 0

Дискриминант (a = 13, b = 16, c = -20)

D = b² - 4ac = 16² - 4(13*-20) = 256 + 1040 = 1296

√D = 36

x = (-b ± √D) / 2a

x = (-16 ± 36) / 26

1) x = (-16 + 36) / 26 = 0.77

2) x = (-16 - 36) / 26 = -2

-2 - не подходит, ответ 0.77 км/ч

Answer 2

Problem Analysis

We are given that a boat traveled 18 km upstream and 14 km downstream, taking a total of 3 hours and 15 minutes. The speed of the boat is given as 10 km/h. We need to find the speed of the current.

Solution

Let's assume the speed of the current is x km/h.

To find the speed of the current, we can use the formula: Speed = Distance / Time

# Upstream Journey

The boat traveled 18 km upstream. The speed of the boat relative to the water is the difference between the boat's speed and the speed of the current: Speed upstream = Boat's speed - Speed of the current

The time taken for the upstream journey is given as 3 hours and 15 minutes, which is equivalent to 3.25 hours.

Using the formula, we can write: 18 km = (10 km/h - x km/h) * 3.25 h

# Downstream Journey

The boat traveled 14 km downstream. The speed of the boat relative to the water is the sum of the boat's speed and the speed of the current: Speed downstream = Boat's speed + Speed of the current

The time taken for the downstream journey is also 3 hours and 15 minutes, or 3.25 hours.

Using the formula, we can write: 14 km = (10 km/h + x km/h) * 3.25 h

Now we have a system of two equations with two unknowns. We can solve this system of equations to find the value of x, which represents the speed of the current.

Solution Steps

1. Solve the first equation for x in terms of 10 km/h and 3.25 h. 2. Solve the second equation for x in terms of 10 km/h and 3.25 h. 3. Set the two expressions for x equal to each other and solve for x.

Let's solve the problem step by step.

Step 1: Solve the first equation for x

Using the formula 18 km = (10 km/h - x km/h) * 3.25 h, we can solve for x.

18 km = (10 km/h - x km/h) * 3.25 h

Dividing both sides by 3.25 h: 18 km / 3.25 h = 10 km/h - x km/h

Simplifying: 5.538 km/h = 10 km/h - x km/h

Adding x km/h to both sides: 5.538 km/h + x km/h = 10 km/h

Combining like terms: 5.538 km/h + x km/h = 10 km/h x km/h = 10 km/h - 5.538 km/h

Simplifying: x km/h = 4.462 km/h

Step 2: Solve the second equation for x

Using the formula 14 km = (10 km/h + x km/h) * 3.25 h, we can solve for x.

14 km = (10 km/h + x km/h) * 3.25 h

Dividing both sides by 3.25 h: 14 km / 3.25 h = 10 km/h + x km/h

Simplifying: 4.308 km/h = 10 km/h + x km/h

Subtracting 10 km/h from both sides: 4.308 km/h - 10 km/h = x km/h

Combining like terms: -5.692 km/h = x km/h

Simplifying: x km/h = -5.692 km/h

Step 3: Set the two expressions for x equal to each other and solve for x

Since we obtained two different values for x in Step 1 and Step 2, we need to determine which value is correct.

Setting the two expressions for x equal to each other: 4.462 km/h = -5.692 km/h

This equation is not possible to solve because the left side is positive and the right side is negative. Therefore, there is no valid solution for x.

Conclusion

Based on the given information, we cannot determine the speed of the current. The problem may have been set up incorrectly or there may be missing information.

Please note that the solution provided is based on the given information and the calculations performed. If there are any errors or missing details, the solution may not be accurate.