Question

Катер прошел расстояние между пристанями туда и обратно за 4,5 ч. Скорость течения реки 2 км/ч. Собственная скорость катера 18 км/ч. Найдите расстояние между пристанями.

Answer 1

Х-шел по течению
4,5-х-шел против течения

(18+2)х=(18-2)(4,5-х)
20х=16 (4,5-х)
20х=72-16х
20х+16х=72
36х=72
х=72/36
х=2 ч-шел по течению

(18+2)*2=20*2=40км

Answer 2

Calculating the Distance Between the Docks

To find the distance between the docks, we can use the formula: distance = speed × time.

First, let's calculate the speed of the boat relative to the water and the speed of the current.

The boat's speed relative to the water is 18 km/h, and the speed of the current is 2 km/h.

The boat's speed relative to the water and current combined is the sum of the boat's speed and the current's speed when they are in the same direction, and the difference when they are in opposite directions.

The boat's speed relative to the water and current combined in the same direction is 18 + 2 = 20 km/h.

The boat's speed relative to the water and current combined in the opposite direction is 18 - 2 = 16 km/h.

Calculating the Total Distance

The total time taken for the round trip is 4.5 hours.

Let's denote the distance between the docks as D.

The time taken to travel from one dock to the other with the current is D / (20 km/h), and against the current is D / (16 km/h).

The total time for the round trip is the sum of the time taken with the current and against the current, which is D / (20 km/h) + D / (16 km/h) = 4.5 hours.

We can solve this equation to find the value of D.

Solving for the Distance

To solve for D, we can use the equation: D / 20 + D / 16 = 4.5.

Multiplying the entire equation by 80 (the least common multiple of 20 and 16) to clear the denominators, we get: 4D + 5D = 360, which simplifies to: 9D = 360.

Dividing both sides by 9, we find: D = 40.

Conclusion

Therefore, the distance between the docks is 40 kilometers.