Question

Расстояние в 30 км один из двух лыжников прошел на 20 мин быстрее другого. Скорость первого лыжника была на 3 км/ч больше скорости второго. Какова была скорость каждого лыжника?

Answer 1

Х км/ч - скорость ІІ лыжника
(х+3) км/ч - скорость І лыжника
t=S:V
20мин=1\3час
30/х - 30/(х+3) = 1/3
Общий знаменатель 3х(х+3)
90х+270-90х=х²+3х
х²+3х-270=0
D=b²-4ac
D=9+1080=1089
х=(-3+33)/2=15(км/ч) - скорость ІІ лыжника
15+3=18(км/ч) - скорость ІІ лыжника

Answer 2

Problem Analysis

We are given that two skiers covered a distance of 30 km, with one skier being 20 minutes faster than the other. The first skier's speed was 3 km/h faster than the second skier's speed. We need to find the speed of each skier.

Solution

Let's assume the speed of the slower skier is x km/h. Since the faster skier is 3 km/h faster, their speed would be x + 3 km/h.

We can use the formula `speed = distance / time` to find the time taken by each skier to cover the distance of 30 km.

For the slower skier: - Speed = x km/h - Distance = 30 km - Time = 30 km / x km/h

For the faster skier: - Speed = x + 3 km/h - Distance = 30 km - Time = 30 km / (x + 3) km/h

We are given that the faster skier took 20 minutes less time than the slower skier. Since 20 minutes is equal to 1/3 of an hour, we can set up the following equation:

30 km / x km/h - 30 km / (x + 3) km/h = 1/3

Now, let's solve this equation to find the values of x and x + 3.

Calculation

To solve the equation, we can use algebraic manipulation. Let's multiply both sides of the equation by the least common multiple (LCM) of the denominators to eliminate the fractions.

LCM of x and x + 3 is 3x(x + 3).

(30 km / x km/h) * 3x(x + 3) - (30 km / (x + 3) km/h) * 3x(x + 3) = (1/3) * 3x(x + 3)

Canceling out the denominators, we get:

30 * 3(x + 3) - 30 * x = x(x + 3)

90x + 270 - 30x = x^2 + 3x

Rearranging the equation:

x^2 + 3x - 90x - 3x - 270 = 0

x^2 - 90x - 270 = 0

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

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a

For our equation, a = 1, b = -90, and c = -270.

x = (-(-90) ± √((-90)^2 - 4 * 1 * -270)) / (2 * 1)

Simplifying further:

x = (90 ± √(8100 + 1080)) / 2

x = (90 ± √9180) / 2

x = (90 ± 95.79) / 2

We have two possible solutions for x:

1. x = (90 + 95.79) / 2 = 185.79 / 2 = 92.895 km/h 2. x = (90 - 95.79) / 2 = -5.79 / 2 = -2.895 km/h

Since speed cannot be negative, we discard the second solution.

Therefore, the speed of the slower skier (x) is approximately 92.895 km/h.

The speed of the faster skier (x + 3) is approximately 92.895 + 3 = 95.895 km/h.

Answer

The speed of the slower skier is approximately 92.895 km/h, and the speed of the faster skier is approximately 95.895 km/h.