Question

теплоход проходит по реке от пристани а до пристани б за 7 часов, а обратно за 5 часов 20 минут. найдите расстояние между пристанями а и б, если скорость течения реки 2км/ч. ответ в километрах

Answer 1

Ответ:

Расстояние между пристанями 89,6 км.

Пошаговое объяснение:

Теплоход проходит по реке от пристани А до пристани В  за 7 часов, а обратно за 5 часов 20 минут. Найти расстояние между пристанями, если скорость течения 2 км/ч.

5 ч 20 мин = $5\dfrac{20}{60}$ ч  =$5\dfrac{1}{3}$ ч  =$\dfrac{16}{3}$ ч.

Решим задачу с помощью уравнения.

Пусть собственная скорость теплохода х км/ч. Тогда (х+2) км/ч - скорость теплохода по течению реки, а ( х-2) км/ч - скорость теплохода против течения реки. Расстояние между пристанями можно определить как расстояние, пройденное против течения

7( х-2) км и      $\dfrac{16}{3} (x+2)$ км-  расстояние, пройденное по течению.

По условию задачи составляем уравнение:

$\dfrac{16}{3} (x+2)=7(x-2)|\cdot 3;\\\\16(x+2)=21(x-2);\\16x+32=21x-42 ;\\16x-21x=-42-32;\\-5x=-74|\cdot(-1);\\5x=74;\\x=74:5;\\x=14,8$

Значит, собственная скорость теплохода 14,8 км/ч.

Найдем расстояние между пристанями.

$7\cdot( 14,8-2)=7\cdot 12,8= 89,6$

Тогда расстояние между пристанями 89,6 км.

#SPJ3

Answer 2

Calculation of Distance between Ports A and B

To find the distance between ports A and B, we need to calculate the speed of the boat in still water. Let's assume the speed of the boat in still water is x km/h.

Given: - Time taken to travel from port A to port B: 7 hours - Time taken to travel from port B to port A: 5 hours 20 minutes (which is equivalent to 5.33 hours) - Speed of the river current: 2 km/h

To calculate the distance between ports A and B, we can use the formula:

Distance = Speed × Time

Let's calculate the distance traveled from port A to port B and from port B to port A separately.

Distance from port A to port B: - Speed of the boat in still water: x km/h - Speed of the river current: 2 km/h - Time taken: 7 hours

The effective speed of the boat while traveling from port A to port B can be calculated as the sum of the boat's speed in still water and the speed of the river current:

Effective speed from A to B = x + 2 km/h

Using the formula Distance = Speed × Time, we can calculate the distance from port A to port B:

Distance from A to B = (x + 2) × 7 km Distance from port B to port A: - Speed of the boat in still water: x km/h - Speed of the river current: 2 km/h - Time taken: 5 hours 20 minutes (which is equivalent to 5.33 hours)

The effective speed of the boat while traveling from port B to port A can be calculated as the difference between the boat's speed in still water and the speed of the river current:

Effective speed from B to A = x - 2 km/h

Using the formula Distance = Speed × Time, we can calculate the distance from port B to port A:

Distance from B to A = (x - 2) × 5.33 km Since the distance from port A to port B is the same as the distance from port B to port A, we can equate the two distances:

(x + 2) × 7 = (x - 2) × 5.33

Simplifying the equation:

7x + 14 = 5.33x - 10.66

1.67x = 24.66

x ≈ 14.77 km/h

Now that we have found the speed of the boat in still water, we can substitute this value back into either of the distance formulas to find the distance between ports A and B.

Using the formula Distance = Speed × Time, let's calculate the distance from port A to port B:

Distance from A to B = (14.77 + 2) × 7 km

Simplifying the equation:

Distance from A to B ≈ 16.77 × 7 km

Distance from A to B ≈ 117.39 km

Therefore, the distance between ports A and B is approximately 117.39 kilometers when the speed of the river current is 2 km/h.

Note: The calculations provided above are based on the given information and assumptions.