Question

из порта одновременно выходят два судна курсы которых лежит на лучах образующих угол 60 градусов Найдите их скорость если известно что скорость первого в три раза больше скорости второго а через два часа после выхода расстояние между ними равнялось 40√7 км

Answer 1

Пусть скорость второго равна х км/ч;
тогда скорость первого равна 3х км/ч;
за 2 часа первый пройдет 2*3х=6х км; второй за 2 часа пройдёт 2х км;
нарисуем треугольник, стороны которого равны 2х; 6х и 40√7;
угол между сторонами 2х и 6х равен 60°;
по теореме косинусов
(40√7)^2=(2х)^2+(6х)^2-2*2х*6х*Cos60°;
11200=40x^2-12x^2;
x^2=11200:28=400;
x=20;
скорость второго равна 20 км/ч;
скорость первого равна 3*20=60 км/ч;
Ответ: 20; 60

Answer 2

Problem Analysis

We are given that two ships are leaving a port simultaneously, and the courses of the ships form an angle of 60 degrees. We need to find the speeds of the ships, given that the speed of the first ship is three times the speed of the second ship. Additionally, after two hours, the distance between the ships is 40√7 km.

Solution

Let's assume the speed of the second ship is v km/h. According to the problem, the speed of the first ship is three times the speed of the second ship, so the speed of the first ship is 3v km/h.

After two hours, the distance between the ships is 40√7 km. We can use the formula distance = speed × time to find the distance traveled by each ship in two hours.

For the first ship: distance1 = speed1 × time = (3v) × 2 = 6v km

For the second ship: distance2 = speed2 × time = v × 2 = 2v km

Since the distance between the ships is the sum of the distances traveled by each ship, we have: distance1 + distance2 = 6v + 2v = 8v = 40√7 km

Now we can solve for v: 8v = 40√7 v = 5√7/2 km/h

Therefore, the speed of the second ship is 5√7/2 km/h and the speed of the first ship is 3v = 15√7/2 km/h.

Answer

The speed of the second ship is 5√7/2 km/h and the speed of the first ship is 15√7/2 km/h.