Question

Теплоход ежедневно совершает рейс между двумя городами . В 8 часов он плывет вверх пл реке, делает остановку 1 ч и в 14 ч того же дня прибывает обратно . Какое расстояние между городами, если скорость течения реки равна 4км/ч, а скорость теплохода 20км/ч

Answer 1

Между 8 и 14 часами 6 часов. Из них пароход стоит 1 час, а плывет 5 часов.
Пксть между городами х км.
Вверх по реке пароход плывет со скоростью 20-4=16км/ч и на путь ввер по реке он тратит х/16 часов
Вниз по реке он плывет со скоростью 20+4=24км/ч и на путь вниз по реке он трартит х/24 часов.
Получаем уравнение
$\frac{x}{16} + \frac{x}{24} =5 \\ \frac{3x}{48} + \frac{2x}{48} =5 \\ \frac{2x+3x}{48} =5 \\ \frac{5x}{48} =5 \\ 5x=5*48 \\ x=48$
Ответ: расстояние между городами 48 км

Answer 2

Calculation of Distance between Cities

To calculate the distance between the two cities, we need to consider the speed of the river current and the speed of the boat.

Given: - Speed of the river current: 4 km/h - Speed of the boat: 20 km/h

We can calculate the effective speed of the boat relative to the ground by subtracting the speed of the river current from the speed of the boat:

Effective speed of the boat = Speed of the boat - Speed of the river current

Therefore, the effective speed of the boat is 20 km/h - 4 km/h = 16 km/h.

To find the distance between the two cities, we need to determine the time it takes for the boat to travel from one city to the other and back.

The boat departs at 8:00 AM and arrives back at the same city at 2:00 PM on the same day. Therefore, the total time for the round trip is 6 hours.

Since the boat travels at an effective speed of 16 km/h, we can calculate the distance using the formula:

Distance = Speed × Time

Distance = 16 km/h × 6 hours

The distance between the two cities is 96 kilometers.

Please note that the above calculation assumes a constant speed throughout the journey and does not take into account any other factors that may affect the actual distance traveled.