Question

№1 В море встретились два корабля. Один ИЗ НИХ шел в Восточном направлении, другой- в северном. Скорость первого на 10 узлов больше, чем второго. Через 2 часа расстояние между ними оказалось равНЫМ 100 МИЛЯМ. Найдите скорость каждого корабля. СРОЧНО!!!!​

Answer 1

Ответ:

Пошаговое объяснение:

x - скорость 1-го корабля, в узлах.

(x-10) - скорость 2-го корабля, в узлах.

По теореме Пифагора a²+b²=c².

(2x)²+(2(x-10))²=100²

4x²+4(x²-20x+100)=10000

x²+x²-20x+100=10000/4                           |2

x²-10x+25-1250=0

x²-10x-1225=0; D=100+4900=5000

x₁=(10-50√2)/2=5-25√2 - ответ не подходит, так как 5-25√2<0

x₂=(10+50√2)/2=5+25√2 - скорость 1-го корабля, в узлах.

5+25√2 -10=25√2 -5 - скорость 2-го корабля, в узлах.

Answer 2

Problem Analysis

Two ships are traveling in the sea, one in the east direction and the other in the north direction. The speed of the first ship is 10 knots faster than the speed of the second ship. After 2 hours, the distance between them is 100 miles. We need to find the speed of each ship.

Solution

Let's denote the speed of the first ship as S1 and the speed of the second ship as S2. We know that the distance traveled is equal to the speed multiplied by time. Therefore, the distance traveled by the first ship in 2 hours is 2S1 and the distance traveled by the second ship in 2 hours is 2S2. Given that the distance between them after 2 hours is 100 miles, we can form the following equation:

2S1 + 2S2 = 100 (Equation 1)

We also know that the speed of the first ship is 10 knots faster than the speed of the second ship:

S1 = S2 + 10 (Equation 2)

We can solve this system of equations to find the speeds of the two ships.

Solving the Equations

Substitute the value of S1 from Equation 2 into Equation 1:

(2S2 + 20) + 2S2 = 100

Simplify the equation:

4S2 + 20 = 100

4S2 = 80

S2 = 20

Now that we have the speed of the second ship, we can find the speed of the first ship using Equation 2:

S1 = 20 + 10 = 30

Answer

So, the speed of the first ship is 30 knots and the speed of the second ship is 20 knots.