Question

Составьте систему уравнений и решите ее способом сложения Моторная лодка проплыла по течению 105 км за 3 часа ,а против тесения 116 км за 4часа.найдите скорость течения и собственную скорость моторной лодки

Answer 1

Система уравнений : 3 * ( x + y ) = 105 ; 4 * ( x - y ) = 116 ; Решение системы способом сложения : Х + у = 35 ; Х - y = 29 ; 2x = 35 + 29 ; x = 46,5 ( км/час ) собственная скорость ; 46,5 - y = 29 ; y = 17,5 ( км/час ) скорость течения

Answer 2

Problem Analysis

To solve this problem, we can set up a system of equations based on the given information. Let's denote the speed of the boat as "b" and the speed of the current as "c". We can use the formula:

Distance = Speed × Time

We have two scenarios: one where the boat is moving with the current and another where it is moving against the current. We can set up the following equations:

1. Moving with the current: 105 = (b + c) × 3 2. Moving against the current: 116 = (b - c) × 4

We can solve this system of equations to find the values of "b" and "c".

Solving the System of Equations

To solve the system of equations, we can use the method of addition. We'll multiply the first equation by 4 and the second equation by 3 to eliminate the "c" variable:

1. 420 = (b + c) × 12 2