Question

За три часа по течению и два часа против течения катер прошел 103 км. Найдите собственную скорость катера, если скорость течения реки равна 3 км/час.

Answer 1

Пусть собственная скорость катера x км/ч. Тогда его скорость по течению реки — x+3 км/ч, а против течения — x-3 км/ч. Значит по течению реки катер прошел 3(x+3) км, а против течения — 2(x-3) км. Зная, что в общем катер прошел 103 км, составим уравнение
3(x+3)+2(x-3)=103
3x+9+2x-6=103
5x+3=103
5x=100
x=20
Значит собственная скорость катера 20 км/ч.
Ответ: 20 км/ч

Answer 2

Составим уравнение:
х-скорость катера
3(х+3)+2(х-3)=103
Раскроем скобки:
3х+9+2х-6=103
Посчитаем:
5х+3=100
Отсюда х=20
Ответ: 20 км/ч
Вот и все С:
Ставь лучшим!

Answer 3

Problem Analysis

We are given that a boat traveled 103 km in 3 hours with the current and 2 hours against the current. The speed of the current is given as 3 km/h. We need to find the speed of the boat in still water.

Solution

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

When the boat is traveling with the current, its effective speed is the sum of its speed in still water and the speed of the current. So, the effective speed is (x + 3) km/h.

When the boat is traveling against the current, its effective speed is the difference between its speed in still water and the speed of the current. So, the effective speed is (x - 3) km/h.

We can use the formula distance = speed × time to calculate the distances traveled in each case.

According to the problem, the boat traveled 103 km in 3 hours with the current and 2 hours against the current. We can set up the following equations:

1. When traveling with the current: (x + 3) × 3 = 103 2. When traveling against the current: (x - 3) × 2 = 103

Let's solve these equations to find the value of x.

Calculation

1. Equation 1: (x + 3) × 3 = 103 - Simplifying: 3x + 9 = 103 - Subtracting 9 from both sides: 3x = 94 - Dividing both sides by 3: x = 31.33

2. Equation 2: (x - 3) × 2 = 103 - Simplifying: 2x - 6 = 103 - Adding 6 to both sides: 2x = 109 - Dividing both sides by 2: x = 54.5

Answer

After solving the equations, we find that the speed of the boat in still water is approximately 31.33 km/h or 54.5 km/h. Please note that there seems to be a discrepancy in the calculations, and further clarification may be needed to determine the correct answer.