Question

Решите задачу с помощью уравнения. ЛОДКА ПРОШЛА З км по течению и 3 км по озеру, затратив на путь по озеру на 1 больше, чем на путь по реке. Скорость течения реки равна 4 км/ч. Найдите собственную скорость лодки.​

Answer 1

3км+3км+4км/ч=6км+4км/ч=10км/ч

Answer 2

Problem Analysis

We are given that a boat traveled a certain distance downstream and then an additional distance on a lake. The boat's speed relative to the water is what we need to find. To solve this problem, we can set up an equation using the given information and solve for the boat's speed.

Solution

Let's denote the boat's speed relative to the water as v km/h. The speed of the river's current is given as 4 km/h.

When the boat is traveling downstream with the current, its effective speed is the sum of its own speed and the speed of the current. Therefore, the effective speed downstream is v + 4 km/h.

When the boat is traveling on the lake, there is no current affecting its speed. Therefore, the effective speed on the lake is just v km/h.

We are also given that the boat spent 1 hour more on the lake than on the river. Let's denote the time spent on the river as t hours. Therefore, the time spent on the lake is t + 1 hours.

The total distance traveled downstream and on the lake is given as z km. We can set up the following equation based on the given information:

Distance downstream + Distance on the lake = Total distance (v + 4)t + (v) (t + 1) = (z)

Simplifying the equation, we get:

vt + 4t + vt + v = z

Combining like terms, we have:

2vt + 4t + v = z

Now we can solve this equation for v, the boat's speed relative to the water.

Calculating the Boat's Speed

To find the boat's speed, we need to know the values of t and z. Unfortunately, these values are not provided in the problem statement. Without these values, we cannot calculate the boat's speed.

Please provide the values of t and z so that we can proceed with the calculation.

If you have any further questions, please let me know!