Question

За 12 часов против течения реки теплоход проходит тот же путь, что за 8 часов по течению. найдите собственную скорость теплохода, если скорость течения 1,5км/ч

Answer 1

Пусть скорость теплохода х, тогда по течению его скорость х+1,5, а против течения х-1,5. Против течения он проходит 12(х-1,5), а по течению 8(х+1,5).
Составим уравнение:
12(х-1,5)=8(х+1,5)
12х-18=8х+12
12х-8х=12+18
4х=30
х=30:4
х=7,5 км/ч собственная скорость теплохода

Проверка: 12(7,5-1,5)=72 км
8(7,5+1,5)=72 км
72=72))

Answer 2

Problem Analysis

We are given that a boat takes the same distance in 12 hours against the current as it does in 8 hours with the current. We need to find the speed of the boat if the current is flowing at a speed of 1.5 km/h.

Solution

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

When the boat is moving against the current, its effective speed is the difference between its speed and the speed of the current. Therefore, the effective speed is (x - 1.5) km/h.

When the boat is moving with the current, its effective speed is the sum of its speed and the speed of the current. Therefore, the effective speed is (x + 1.5) km/h.

We are given that the boat takes the same distance in 12 hours against the current as it does in 8 hours with the current. This means that the distance traveled is the same in both cases.

Using the formula distance = speed × time, we can set up the following equation:

(x - 1.5) × 12 = (x + 1.5) × 8

Let's solve this equation to find the value of x.

Calculation

Expanding the equation:

12x - 18 = 8x + 12

Simplifying the equation:

12x - 8x = 12 + 18

4x = 30

Dividing both sides by 4:

x = 7.5

Answer

The speed of the boat is 7.5 km/h.

Explanation

When the boat is moving against the current at a speed of 7.5 km/h, its effective speed is (7.5 - 1.5) = 6 km/h. In 12 hours, it covers a distance of 6 km/h × 12 h = 72 km.

When the boat is moving with the current at a speed of 7.5 km/h, its effective speed is (7.5 + 1.5) = 9 km/h. In 8 hours, it covers a distance of 9 km/h × 8 h = 72 km.

Therefore, the boat covers the same distance in both cases, confirming our solution.