Question

Помогите решить: из города B вышли одновременно два лыжника. один направился на север, а другой на восток. через 2 часа расстояние между ними стало равно 20 км, при чем первый лыжник прошел на 4 км больше, чем второй. с кской скоростью шел первый лыжник?

Answer 1

Первый прошел 20-4=16
16/2=8
первый прошел 8+4=12, тогда второй 8
12/2=6км/час прошел первый лыжник, второй 8/2=4км/час

Answer 2

Problem Analysis

Two skiers start simultaneously from the same point. One skier goes north, while the other skier goes east. After 2 hours, the distance between them is 20 km, with the first skier having traveled 4 km more than the second skier. We need to determine the speed at which the first skier is traveling.

Solution

Let's assume the speed of the first skier is x km/h. Since the skiers started at the same time, the second skier's speed will be x - 4 km/h (as the first skier traveled 4 km more than the second skier).

After 2 hours, the first skier has traveled a distance of 2x km (since speed * time = distance). The second skier has traveled a distance of (x - 4) * 2 km.

According to the problem, the distance between them is 20 km. Therefore, we can set up the following equation:

2x^2 + 4(x - 4)^2 = 20^2

Simplifying the equation:

2x^2 + 4(x^2 - 8x + 16) = 400

2x^2 + 4x^2 - 32x + 64 = 400

6x^2 - 32x - 336 = 0

Now we can solve this quadratic equation to find the value of x.

Quadratic Equation Solution

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 6, b = -32, and c = -336.

Calculating the discriminant: D = b^2 - 4ac = (-32)^2 - 4 * 6 * (-336) = 32^2 + 4 * 6 * 336 = 1024 + 8064 = 9088.

Since the discriminant is positive, there are two real solutions for x.

Calculating the solutions:

x = (-(-32) ± √(9088)) / (2 * 6)

x = (32 ± √9088) / 12

x ≈ (32 ± 95.33) / 12

Simplifying:

x ≈ 127.33 / 12 ≈ 10.61 or x ≈ -31.33 / 12 ≈ -2.61

Since speed cannot be negative, the first skier's speed is approximately 10.61 km/h.

Answer

The first skier is traveling at a speed of approximately 10.61 km/h.