Question

От пристани по течению реки отправилась на лодке группа туристов, рассчитывая вернуться через 4 часа. Скорость лодки в стоячей воде составляет 10 км/ч, 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?

Answer 1

Скорость по течению 10+2=12
скорость против течения 10-2=8
время в пути 4-2=2
t1+t2=2
t1*12=t2*8  t2=1,5t1
2,5t1=2
t1=4/5
S=4/5*12=9,6 км

Answer 2

Calculation of the Maximum Distance the Tourists Can Sail

To calculate the maximum distance the tourists can sail from the pier, we need to consider the speed of the boat in still water and the speed of the river current.

Given: - Boat speed in still water: 10 km/h - Speed of the river current: 2 km/h - Time for the round trip: 4 hours - Time for the break: 2 hours

To find the maximum distance, we need to determine the time it takes for the boat to travel upstream and downstream.

Let's assume: - Distance upstream = x km - Distance downstream = y km

Calculating the Time for the Upstream Journey

The speed of the boat relative to the ground when traveling upstream is the difference between the boat's speed in still water and the speed of the river current.

Relative speed upstream = Boat speed in still water - Speed of the river current = 10 km/h - 2 km/h = 8 km/h

The time taken to travel upstream can be calculated using the formula: time = distance / speed.

Time taken to travel upstream = x km / 8 km/h = x/8 hours

Calculating the Time for the Downstream Journey

The speed of the boat relative to the ground when traveling downstream is the sum of the boat's speed in still water and the speed of the river current.

Relative speed downstream = Boat speed in still water + Speed of the river current = 10 km/h + 2 km/h = 12 km/h

The time taken to travel downstream can be calculated using the formula: time = distance / speed.

Time taken to travel downstream = y km / 12 km/h = y/12 hours

Total Time for the Trip

The total time for the round trip, including the break, is given as 4 hours.

Total time = Time taken to travel upstream + Time taken to travel downstream + Time for the break

4 hours = x/8 hours + y/12 hours + 2 hours

Simplifying the equation:

4 = (3x + 2y) / 24

Multiplying both sides by 24:

96 = 3x + 2y

Finding the Maximum Distance

To find the maximum distance, we need to maximize the value of y while satisfying the equation 96 = 3x + 2y.

Since we want to maximize y, we can set x = 0 and solve for y:

96 = 2y

y = 48

Therefore, the maximum distance the tourists can sail from the pier is 48 kilometers.

Please note that this calculation assumes a constant speed throughout the journey and does not take into account other factors such as wind or changes in the river current.