Question

Решение задач с помощью систем линейных уравнений. Моторная лодка проплывает от одной речной пристани до другой за 4 часа, а обратно-за 5 часов. Найди скорость движения лодки в стоячей воде, если расстояние между этими пристанями равно 80 км.

Answer 1

80÷4=20 км/ч скорость по течению.
80÷5=16 км/ч скорость против течения.
(20-16)÷2=2 км/ч скорость реки.
20-2=18 км/ч скорость движения лодки в стоячей воде.
Ответ: 18 км/ч.

Answer 2

Solving the Problem Using Systems of Linear Equations

To solve this problem, we can use the concept of relative speed and set up a system of linear equations.

Let's denote the speed of the boat in still water as x km/h and the speed of the current as y km/h.

Setting Up the Equations

1. When the boat travels downstream (from the first dock to the second dock), the effective speed is the sum of the boat's speed and the speed of the current. The time taken is 4 hours. - Equation 1: (x + y) * 4 = 80

2. When the boat travels upstream (from the second dock back to the first dock), the effective speed is the difference between the boat's speed and the speed of the current. The time taken is 5 hours. - Equation 2: (x - y) * 5 = 80

Solving the Equations

We can solve these two equations simultaneously to find the values of x and y.

Finding the Speed of the Boat in Still Water

By solving the system of equations, we can find the speed of the boat in still water.

Let's proceed with the calculations.