Question

Расстояние между двумя пунктами по реке равно 14 км. Лодка проходит этот путь вниз по реке за 2ч, а вверх по реке - за 2ч 48мин. Найдите собственную скорость лодки в скорость течения реки. (РЕШИТЕ БЕЗ Х, ПОЖАЛУЙСТА)

Answer 1

14:2=7км/ч скорость лодки по течению реки
14:2 4/5=14 *5/14 =5км/ч скорость лодки против течения реки
(7-5):2=2:2=1км/ч скорость течения реки
7-1=6км/ч собственная скорость лодки

Answer 2

Problem Analysis

We are given that the distance between two points on a river is 14 km. The boat takes 2 hours to travel downstream and 2 hours 48 minutes to travel upstream. We need to find the speed of the boat in still water and the speed of the river's current.

Solution

Let's assume the speed of the boat in still water is x km/h and the speed of the river's current is y km/h.

When the boat is traveling downstream, its effective speed is the sum of its speed in still water and the speed of the current. So, the boat's effective speed is (x + y) km/h.

When the boat is traveling upstream, its effective speed is the difference between its speed in still water and the speed of the current. So, the boat's effective speed is (x - y) km/h.

We can use the formula speed = distance / time to calculate the boat's speed in still water and the speed of the river's current.

Calculation

Let's calculate the boat's speed in still water and the speed of the river's current.

1. Downstream speed: - Distance = 14 km - Time = 2 hours - Speed = Distance / Time = 14 km / 2 hours = 7 km/h downstream

2. Upstream speed: - Distance = 14 km - Time = 2 hours 48 minutes = 2.8 hours - Speed = Distance / Time = 14 km / 2.8 hours = 5 km/h upstream

Now, we can solve the following system of equations to find the values of x and y:

Equation 1: (x + y) = 7 (downstream speed) Equation 2: (x - y) = 5 (upstream speed)

Adding Equation 1 and Equation 2, we get: (x + y) + (x - y) = 7 + 5 Simplifying, we get: 2x = 12 Dividing both sides by 2, we get: x = 6

Substituting the value of x into Equation 1, we get: (6 + y) = 7 Simplifying, we get: y = 1

Therefore, the boat's speed in still water is 6 km/h and the speed of the river's current is 1 km/h.

Answer

The boat's speed in still water is 6 km/h and the speed of the river's current is 1 km/h.