Question

С аэродрома одновременно вылетели 2 самолета: один - на запад, другой - на юг. Через 2 часа расстояние между ними было 2000км. Найдите сумму скоростей самолетов, если скорость одного из них составляла 75% скорости другого.

Answer 1

X - скорость одного, 0,75X - скорость другого

X*2 + 0,75X*2 = 2000

3,5 X = 2000

X = 571,43 (км/час)

2X = 428, 5 (км/час)

 

Answer 2

Calculating the Sum of the Speeds of the Airplanes

To find the sum of the speeds of the airplanes, we can use the concept of relative speed. Let's denote the speed of the first airplane as x and the speed of the second airplane as y. Given that the speed of one airplane is 75% of the speed of the other, we can express the speed of the second airplane as 1.75x.

Calculating the Relative Speed

When two objects move in different directions, their relative speed is the sum of their individual speeds. In this case, the relative speed between the two airplanes after 2 hours is 2000 km.

Using the formula for relative speed, we can express the relative speed as the sum of the speeds of the airplanes in the given directions:

Relative speed = Speed of the first airplane + Speed of the second airplane

Solving for the Sum of the Speeds

Given that the relative speed is 2000 km and the speed of one airplane is 75% of the speed of the other, we can set up the equation to solve for the sum of the speeds.

Let's denote the speed of the first airplane as x and the speed of the second airplane as y. Since the speed of one airplane is 75% of the speed of the other, we can express the speed of the second airplane as 1.75x.

Using the formula for relative speed, we can express the relative speed as the sum of the speeds of the airplanes in the given directions:

Relative speed = Speed of the first airplane + Speed of the second airplane

Given that the relative speed is 2000 km and the speed of one airplane is 75% of the speed of the other, we can set up the equation to solve for the sum of the speeds.

The equation can be expressed as: 2x + 2(1.75x) = 2000

Solving for x: 2x + 3.5x = 2000 5.5x = 2000 x = 2000 / 5.5 x = 363.64 km/h

Now that we have found the speed of the first airplane, we can calculate the speed of the second airplane: y = 1.75x y = 1.75 * 363.64 y = 636.36 km/h

Calculating the Sum of the Speeds

Finally, we can calculate the sum of the speeds of the airplanes: Sum of the speeds = Speed of the first airplane + Speed of the second airplane Sum of the speeds = 363.64 km/h + 636.36 km/h Sum of the speeds = 1000 km/h

Therefore, the sum of the speeds of the airplanes is 1000 km/h.