Question

Катер прошёл расстояние между пристанями за 40 минут против течения реки и за 24 минут по течению реки . Найти расстояние между пристанями, если скорость течения реки 1,5 км/мин Чему равняется Х? 1,5???

Answer 1

1)40+24=64
2)64·1,5=96-расстояние между пристаниями

Answer 2

Problem Analysis

We are given that a boat traveled a certain distance between two piers in 40 minutes against the current of a river and in 24 minutes with the current of the river. We need to find the distance between the piers, given that the speed of the river's current is 1.5 km/min.

Solution

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

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. Therefore, the boat's speed against the current is (x - 1.5) km/min.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. Therefore, the boat's speed with the current is (x + 1.5) km/min.

We can use the formula distance = speed × time to calculate the distance traveled by the boat in both scenarios.

Let's calculate the distances:

- Distance traveled against the current: (x - 1.5) km/min × 40 min - Distance traveled with the current: (x + 1.5) km/min × 24 min

Since the distance between the piers is the same in both scenarios, we can equate the two distances and solve for x.

Calculation

Let's calculate the distance between the piers.

Distance traveled against the current = Distance traveled with the current

((x - 1.5) km/min × 40 min) = ((x + 1.5) km/min × 24 min)

Simplifying the equation:

40(x - 1.5) = 24(x + 1.5)

Expanding and rearranging the equation:

40x - 60 = 24x + 36

40x - 24x = 36 + 60

16x = 96

x = 96 / 16

x = 6

Therefore, the speed of the boat in still water is 6 km/min.

Now, let's calculate the distance between the piers using the speed of the boat in still water.

Distance traveled against the current = (6 - 1.5) km/min × 40 min

Distance traveled with the current = (6 + 1.5) km/min × 24 min

Calculation

Let's calculate the distance between the piers.

Distance traveled against the current = (6 - 1.5) km/min × 40 min

Distance traveled with the current = (6 + 1.5) km/min × 24 min

Distance traveled against the current = 4.5 km/min × 40 min

Distance traveled with the current = 7.5 km/min × 24 min

Distance traveled against the current = 180 km

Distance traveled with the current = 180 km

Therefore, the distance between the piers is 180 km.

Answer

The distance between the piers is 180 km. The value of x is 6.