Question

Решить задачу с объяснением, и уравнением. Расстояние от одной пристани на реке до другой теплоход проходит за 6 часов, а обратно за 5 часов. Найдите собственную скорость теплохода, если скорость течения реки равна 2 км/ч.РЕШИТЕ СРОЧНО УМЛЯЮ!!!ПОООООООЖААААЛУЙСТАААААА!!!!!!! ОЧЕНЬ НУЖНО

Answer 1

Пусть х км/ч - собственная скорость теплохода, х>0

Тогда

(х+2)км/ч - скорость по течению

(х-2)км/ч - скорость против течения

(х-2)*6 км - путь пройденный против течения

(х+2)*5 км - путь пройденный по течению

Тк теплоход проходит один и тот же путь

6(х-2)=5(х+2)

6х-12=5х+10

6х-5х=10+12

х=22 км/ч - собственная скорость теплохода

Ответ: 22 км/ч

Answer 2

Problem Analysis

To solve this problem, we can use the formula:

Distance = Speed × Time

Let's assume the speed of the boat is B km/h and the speed of the river current is C km/h.

When the boat is moving downstream (from one pier to another), the effective speed of the boat is the sum of its own speed and the speed of the river current. So, the effective speed is B + C km/h.

When the boat is moving upstream (from the other pier back to the starting pier), the effective speed of the boat is the difference between its own speed and the speed of the river current. So, the effective speed is B - C km/h.

We are given that the boat takes 6 hours to travel from one pier to another and 5 hours to travel back. We also know that the speed of the river current is 2 km/h.

Solution

Let's solve the problem step by step:

1. When the boat is moving downstream: - Distance = Speed × Time - Distance downstream = (B + C) × 6

2. When the boat is moving upstream: - Distance = Speed × Time - Distance upstream = (B - C) × 5

We know that the distance downstream is equal to the distance upstream. So, we can set up the following equation:

(B + C) × 6 = (B - C) × 5

Now, let's solve this equation to find the speed of the boat.

Solving the Equation

Expanding the equation, we get:

6B + 6C = 5B - 5C

Combining like terms, we get:

6B - 5B = -5C - 6C

Simplifying further, we get:

B = -11C

Now, we substitute the value of the speed of the river current, which is 2 km/h:

B = -11(2)

Simplifying, we get:

B = -22

Since speed cannot be negative, we discard the negative solution. Therefore, the speed of the boat is 22 km/h.

Answer

The speed of the boat is 22 km/h.

Please note that the negative value obtained during the calculation is discarded because speed cannot be negative.