Question

О пристани по течению реки отправилась на лодке группа туристов,рассчитывая вернуться через 4 ч.Скорость лодки в стоячей воде составляет 10 км/,а скорость течения-2 км/ч. На какое наибольшее расстояние туристы могут отплыть от пристани, если они хотят перед возвращением сделать привал на 2 ч? Спасибо)) :З

Answer 1

4-2=2 ч на путь туда и обратно.
t1 - время по теч.
t2 - против
t1+t2=2
(10+2)t1=(10-2)t2
12t1=8t2
t1=$\frac{8}{12} = \frac{2}{3}$t2
t2+$\frac{2}{3}$t2=2
$\frac{5}{3}$t2=2
t2=$2: \frac{5}{3} =2* \frac{3}{5} = \frac{6}{5} =1,2$ч
S=Vпротив*t2=8*1,2=9,6 км

Answer 2

Problem Analysis

A group of tourists set off on a boat from a dock, intending to return after 4 hours. The boat's speed in still water is 10 km/h, and the speed of the river current is 2 km/h. The question is: what is the maximum distance the tourists can sail away from the dock if they want to take a 2-hour break before returning?

Solution

To solve this problem, we need to consider the speed of the boat in relation to the speed of the river current. When the boat is moving upstream (against the current), its effective speed is reduced, and when it is moving downstream (with the current), its effective speed is increased.

Let's calculate the maximum distance the tourists can sail away from the dock by considering the time they have and the speed of the boat and the current.

1. Calculating the time spent sailing upstream: - The boat's speed in still water is 10 km/h, and the speed of the river current is 2 km/h. - When the boat is moving upstream, its effective speed is the difference between the boat's speed and the current's speed: 10 km/h - 2 km/h = 8 km/h. - The time spent sailing upstream is 4 hours - 2 hours (break time) = 2 hours. - Using the formula: time = distance / speed, we can calculate the distance traveled upstream: distance = time * speed. - Therefore, the distance traveled upstream is 2 hours * 8 km/h = 16 km.

2. Calculating the time spent sailing downstream: - When the boat is moving downstream, its effective speed is the sum of the boat's speed and the current's speed: 10 km/h + 2 km/h = 12 km/h. - The time spent sailing downstream is 2 hours (break time). - Using the formula: time = distance / speed, we can calculate the distance traveled downstream: distance = time * speed. - Therefore, the distance traveled downstream is 2 hours * 12 km/h = 24 km.

3. Calculating the maximum distance from the dock: - The maximum distance the tourists can sail away from the dock is the sum of the distances traveled upstream and downstream: 16 km + 24 km = 40 km.

Answer

The tourists can sail a maximum distance of 40 km away from the dock if they want to take a 2-hour break before returning.