Question

Туристы проплыли на лодке от лагеря некоторое расстояние вверх по течению реки, затем причали к берегу и, прогуляв 3 часа, вернулись обратно через 5 часов от начала путешествия. На какое расстояние от лагеря они отплыли, если скорость течения реки равна 2 км/ч, а собственная скорость лодки 8 км/ч?

Answer 1

Решение
Туристы затратили на путь по реке 5-3=2 часа. Скорость лодки по течению реки равна 8+2=10 км/ч, а против течения реки 8-2=6 км/ч. Время, за которое туристы проплыли расстояние S по течению реки равно $\frac{S}{10}$ часов, а против течения реки $\frac{S}{6}$ часов. Всего 2 часа.
Составим и решим уравнение:
$\frac{S}{6}$ + $\frac{S}{10}$=2
$\frac{10S}{60}$+$\frac{6S}{60}$ = 2
$\frac{16S}{60}$ = 2
16S=2*60
16S=120
S=120:16
S=7,5 км - отплыли туристы от лагеря.
ОТВЕТ: туристы отплыли от лагеря на 7,5 км.
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Проверка:
7,5:6=1,25 часа (1,25*60=75 минут)
7,5:10=0,75 часа (0,75*60=45 минут)
1,25 часа + 0,75 часа=2 часа (75+45=120 минут:60=2 часа)

Answer 2

Problem Analysis

The problem states that tourists traveled a certain distance upstream on a river in a boat, then docked on the shore and walked for 3 hours before returning back to the starting point in the boat. The speed of the river current is given as 2 km/h, and the speed of the boat is given as 8 km/h. We need to determine the distance from the campsite where they started.

Solution

To solve this problem, we can use the formula: distance = speed × time.

Let's break down the problem into two parts: the distance traveled upstream and the distance traveled downstream.

1. Distance traveled upstream: - The speed of the boat relative to the ground is the difference between the boat's speed and the speed of the river current: 8 km/h - 2 km/h = 6 km/h. - The time spent traveling upstream is given as 5 hours. - Using the formula, the distance traveled upstream is: distance = speed × time = 6 km/h × 5 h = 30 km.

2. Distance traveled downstream: - The speed of the boat relative to the ground is the sum of the boat's speed and the speed of the river current: 8 km/h + 2 km/h = 10 km/h. - The time spent traveling downstream is given as 3 hours. - Using the formula, the distance traveled downstream is: distance = speed × time = 10 km/h × 3 h = 30 km.

Since the distance traveled upstream and downstream is the same, we can conclude that the distance from the campsite where they started is 30 km.

Answer

The tourists traveled a distance of 30 km from the campsite where they started.