Question

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

Answer 1

Скорость по течению равна 8+2=10 км/ч
Скорость против течения равна 8-2=6 км/ч
Обозначим расстояние, которое плыли на лодке за х.
Всё время путешествия 5 часов, время, которое плыли по течению х/10, время, которое гуляли 3 часа, время, которое плыли против течения х/6. Составим уравнение:
х/10+3+х/6 =5
Избавимся от знаменателя, обищй знаменатель 10:
х+3*10+х*1.6=5*10
2.6х=50-30

 2.6x=20

х=7.5 .
Ответ: 7,5  км

Answer 2

пусть x км расстояние от лагеря
тогда время, затраченное на дорогу туда = x/(8+2) часов
время, затраченное на дорогу обратно = x/(8-2)
зная, что всего на прогулку затрачено 5 часов и продолжительность остановки, составим уравнение:
х/(8+2)+х/(8-2)+3=5
х/10+х/6=2
домножим на 30
3х+5х=60
8х=60
х=7,5 

Answer 3

Problem Analysis

The problem states that tourists traveled a certain distance upstream on a river in a boat, then docked on the shore, walked for 3 hours, and returned back to the starting point in 5 hours. We need to determine the distance they traveled upstream from the camp.

Solution

Let's assume the distance traveled upstream from the camp is x km.

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

The speed of the boat relative to the water is the difference between the boat's speed and the speed of the river current. In this case, the speed of the boat relative to the water is 8 km/h - 2 km/h = 6 km/h.

The time it took to travel upstream is given as 3 hours, so the distance traveled upstream is 6 km/h × 3 hours = 18 km.

To return back to the starting point, the boat's speed relative to the water is the sum of the boat's speed and the speed of the river current, which is 8 km/h + 2 km/h = 10 km/h.

The time it took to return is given as 5 hours, so the distance traveled downstream is 10 km/h × 5 hours = 50 km.

Since the boat traveled 18 km upstream and 50 km downstream, the total distance traveled is 18 km + 50 km = 68 km.

Therefore, the tourists traveled a distance of 68 km upstream from the camp.

Answer

The tourists traveled a distance of 68 km upstream from the camp.

Explanation

The tourists traveled upstream at a speed of 8 km/h relative to the water, while the river current was flowing at a speed of 2 km/h. This resulted in a net speed of 6 km/h upstream. They traveled for 3 hours upstream, covering a distance of 18 km. Then, they returned downstream at a speed of 10 km/h (8 km/h boat speed + 2 km/h current speed) and traveled for 5 hours, covering a distance of 50 km. The total distance traveled was 18 km upstream + 50 km downstream = 68 km.