Question

Туристы проплыли на лодке 2,4 ч по течению реки и 1,8 часа против течения, при этом по течению их путь был на 14,1 км больше, чем против течения.Найдите скорость лодки в стоячей воде, если скорость течения реки реки равна 2,5км/ч

Answer 1

2.4 * ( X + 2.5) - 14.1 = 1.8 * ( X - 2.5)
2.4X + 6 - 14.1 = 1.8X - 4.5 
2.4X - 8.1 = 1.8X - 4.5 
0.6X = 3.6 
X = 6
ответ 6 км\час скорость лодки в стоячей воде

Answer 2

Problem Analysis

We are given that tourists traveled on a boat for 2.4 hours with the current of the river and 1.8 hours against the current. The distance traveled with the current was 14.1 km more than the distance traveled against the current. We need to find the speed of the boat in still water, given that the speed of the river current is 2.5 km/h.

Solution

Let's assume the speed of the boat in still water is x km/h.

When traveling with the current, the effective speed of the boat is the sum of the speed of the boat in still water and the speed of the current, which is (x + 2.5) km/h. The time taken to travel with the current is 2.4 hours.

When traveling against the current, the effective speed of the boat is the difference between the speed of the boat in still water and the speed of the current, which is (x - 2.5) km/h. The time taken to travel against the current is 1.8 hours.

We are given that the distance traveled with the current is 14.1 km more than the distance traveled against the current.

Using the formula distance = speed × time, we can set up the following equations:

Equation 1: (x + 2.5) × 2.4 = (x - 2.5) × 1.8 + 14.1

Simplifying Equation 1, we get:

2.4x + 6 = 1.8x - 4.5 + 14.1

0.6x = 11.4

x = 19

Therefore, the speed of the boat in still water is 19 km/h.

Answer

The speed of the boat in still water is 19 km/h.

Explanation

The speed of the boat in still water can be found by setting up equations based on the given information. By solving these equations, we find that the speed of the boat in still water is 19 km/h.